{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:02:27Z","timestamp":1759147347517},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,3,5]],"date-time":"2022-03-05T00:00:00Z","timestamp":1646438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,5]],"date-time":"2022-03-05T00:00:00Z","timestamp":1646438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s10998-022-00450-0","type":"journal-article","created":{"date-parts":[[2022,3,5]],"date-time":"2022-03-05T21:02:31Z","timestamp":1646514151000},"page":"448-473","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Cuf products and cuf sums of (quasi-) metrizable spaces in $${\\mathbf {Z}}{\\mathbf {F}}$$"],"prefix":"10.1007","volume":"85","author":[{"given":"Kyriakos","family":"Keremedis","sequence":"first","affiliation":[]},{"given":"Eliza","family":"Wajch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,5]]},"reference":[{"key":"450_CR1","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/76904","author":"A Andrikopoulos","year":"2007","unstructured":"A. Andrikopoulos, The quasimetrization problem in the (bi)topological spaces. Int. J. Math. Math. Sci. (2007). https:\/\/doi.org\/10.1155\/2007\/76904","journal-title":"Int. J. Math. Math. Sci."},{"key":"450_CR2","doi-asserted-by":"publisher","first-page":"175","DOI":"10.4153\/CJM-1951-022-3","volume":"3","author":"RH Bing","year":"1951","unstructured":"R.H. Bing, Metrization of topological spaces. Can. J. Math. 3, 175\u2013186 (1951)","journal-title":"Can. J. Math."},{"key":"450_CR3","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1002\/malq.19850312507","volume":"31","author":"N Brunner","year":"1985","unstructured":"N. Brunner, Products of compact spaces in the least permutation model. Z. Math. Logik Grundlagen Math. 31, 441\u2013448 (1985)","journal-title":"Z. Math. Logik Grundlagen Math."},{"key":"450_CR4","volume-title":"Hausdorff Compactifications","author":"RE Chandler","year":"1976","unstructured":"R.E. Chandler, Hausdorff Compactifications (Marcel Dekker, New York, 1976)"},{"key":"450_CR5","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1090\/S0002-9939-1984-0733418-9","volume":"90","author":"PJ Collins","year":"1984","unstructured":"P.J. Collins, A.W. Roscoe, Criteria for metrisability. Proc. Amer. Math. Soc. 90, 631\u2013640 (1984)","journal-title":"Proc. Amer. Math. Soc."},{"key":"450_CR6","unstructured":"S. M. Corson, The independence of Stone\u2019s theorem from the Boolean prime ideal theorem, arxiv.org\/pdf\/2001.06513pdf"},{"key":"450_CR7","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1002\/malq.200310049","volume":"49","author":"O De la Cruz","year":"2003","unstructured":"O. De la Cruz, E.J. Hall, P. Howard, K. Keremedis, J.E. Rubin, Metric spaces and the axiom of choice. Math. Logic Quart. 49, 455\u2013466 (2003)","journal-title":"Math. Logic Quart."},{"key":"450_CR8","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1002\/malq.200710073","volume":"54","author":"O De la Cruz","year":"2008","unstructured":"O. De la Cruz, E.J. Hall, P. Howard, K. Keremedis, J.E. Rubin, Unions and the axiom of choice. Math. Logic Quart. 54, 652\u2013665 (2008)","journal-title":"Math. Logic Quart."},{"key":"450_CR9","first-page":"101","volume":"95","author":"EK van Douwen","year":"1985","unstructured":"E.K. van Douwen, Horrors of topology without AC: a nonnormal orderable space. Proc. Amer. Math. Soc. 95, 101\u2013105 (1985)","journal-title":"Proc. Amer. Math. Soc."},{"key":"450_CR10","volume-title":"General Topology, (Sigma Series in Pure Mathematics 6","author":"R Engelking","year":"1989","unstructured":"R. Engelking, General Topology, (Sigma Series in Pure Mathematics 6 (Heldermann, Berlin, 1989)"},{"key":"450_CR11","volume-title":"Quasi-Uniform Spaces","author":"P Fletcher","year":"1982","unstructured":"P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces (Marcel Dekker, New York, 1982)"},{"key":"450_CR12","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0166-8641(95)90010-1","volume":"63","author":"C Good","year":"1995","unstructured":"C. Good, I. Tree, Continuing horrors of topology without choice. Topol. Appl. 63, 79\u201390 (1995)","journal-title":"Topol. Appl."},{"key":"450_CR13","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1090\/S0002-9939-98-04163-X","volume":"126","author":"C Good","year":"1998","unstructured":"C. Good, I. Tree, W. Watson, On Stone\u2019s theorem and the axiom of choice. Proc. Amer. Math. Soc. 126, 1211\u20131218 (1998)","journal-title":"Proc. Amer. Math. Soc."},{"key":"450_CR14","doi-asserted-by":"publisher","first-page":"3420","DOI":"10.1016\/j.topol.2006.03.003","volume":"153","author":"G Gutierres","year":"2006","unstructured":"G. Gutierres, What is a first countable space? Topol. Appl. 153, 3420\u20133429 (2006)","journal-title":"Topol. Appl."},{"key":"450_CR15","volume-title":"Axiom of Choice, (Lecture Notes in Mathematics 1876","author":"H Herrlich","year":"2006","unstructured":"H. Herrlich, Axiom of Choice, (Lecture Notes in Mathematics 1876 (Springer, New York, 2006)"},{"key":"450_CR16","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1002\/(SICI)1521-3870(200005)46:2<219::AID-MALQ219>3.0.CO;2-2","volume":"46","author":"P Howard","year":"2000","unstructured":"P. Howard, K. Keremedis, J.E. Rubin, A. Stanley, Paracompactness of metric spaces and the axiom of multiple choice. Math. Logic Quart. 46, 219\u2013232 (2000)","journal-title":"Math. Logic Quart."},{"key":"450_CR17","doi-asserted-by":"crossref","unstructured":"P. Howard, J. E. Rubin, Consequences of the axiom of choice, (Math. Surveys and Monographs 59, A.M.S., Providence R.I., 1998)","DOI":"10.1090\/surv\/059"},{"key":"450_CR18","unstructured":"P. Howard, J. E. Rubin, Other forms added to the ones from [17], I. Dimitriou web page https:\/\/cgraph.inters.co\/names-and-statements"},{"key":"450_CR19","doi-asserted-by":"publisher","first-page":"107591","DOI":"10.1016\/j.topol.2021.107591","volume":"290","author":"P Howard","year":"2021","unstructured":"P. Howard, E. Tachtsis, On metrizability and compactness of certain products without the Axiom of Choice. Topol. Appl. 290, 107591 (2021)","journal-title":"Topol. Appl."},{"key":"450_CR20","volume-title":"The Axiom of Choice","author":"T Jech","year":"1973","unstructured":"T. Jech, The Axiom of Choice (North-Holland Publishing Co., Amsterdam, 1973)"},{"key":"450_CR21","unstructured":"T. Jech,  Set Theory. The Third Millennium Edition, revised and expanded, (Springer Monographs in Mathematics, Springer, Berlin, 2003)"},{"key":"450_CR22","doi-asserted-by":"publisher","first-page":"75","DOI":"10.4064\/fm-37-1-75-76","volume":"37","author":"JL Kelley","year":"1950","unstructured":"J.L. Kelley, The Tychonoff product theorem implies the axiom of choice. Fund. Math. 37, 75\u201376 (1950)","journal-title":"Fund. Math."},{"key":"450_CR23","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1112\/plms\/s3-13.1.71","volume":"13","author":"JC Kelly","year":"1963","unstructured":"J.C. Kelly, Bitopological spaces. Proc. London Math. Soc. 13, 71\u201389 (1963)","journal-title":"Proc. London Math. Soc."},{"key":"450_CR24","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1007\/s001530100094","volume":"40","author":"K Keremedis","year":"2001","unstructured":"K. Keremedis, Disasters in topology without the axiom of choice. Arch. Math. Logic 40, 569\u2013580 (2001)","journal-title":"Arch. Math. Logic"},{"key":"450_CR25","doi-asserted-by":"publisher","first-page":"109","DOI":"10.4064\/ba8087-12-2016","volume":"64","author":"K Keremedis","year":"2016","unstructured":"K. Keremedis, Some notions of separability of metric spaces in ZF and their relation to compactness. Bull. Pol. Acad. Sci. Math. 64, 109\u2013136 (2016)","journal-title":"Bull. Pol. Acad. Sci. Math."},{"key":"450_CR26","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1002\/1521-3870(200101)47:1<117::AID-MALQ117>3.0.CO;2-N","volume":"47","author":"K Keremedis","year":"2001","unstructured":"K. Keremedis, E. Tachtsis, Compact metric spaces and weak forms of the axiom of choice. Math. Logic Quart. 47, 117\u2013128 (2001)","journal-title":"Math. Logic Quart."},{"key":"450_CR27","first-page":"15","volume":"4","author":"K Keremedis","year":"2001","unstructured":"K. Keremedis, E. Tachtsis, On Loeb and weakly Loeb Hausdorff spaces. Sci. Math. Jpn. Online 4, 15\u201319 (2001)","journal-title":"Sci. Math. Jpn. Online"},{"key":"450_CR28","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/malq.200410011","volume":"51","author":"K Keremedis","year":"2005","unstructured":"K. Keremedis, E. Tachtsis, Countable sums and products of metrizable spaces in $${\\mathbf{Z}}{\\mathbf{F}}$$. Math. Logic Quart. 51, 95\u2013103 (2005)","journal-title":"Math. Logic Quart."},{"key":"450_CR29","doi-asserted-by":"crossref","unstructured":"K. Keremedis, E. Tachtsis, Cellularity of infinite Hausdorff spaces in ZF, Topology Appl., 274, 107104 (2020)","DOI":"10.1016\/j.topol.2020.107104"},{"key":"450_CR30","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.topol.2019.02.046","volume":"258","author":"K Keremedis","year":"2019","unstructured":"K. Keremedis, E. Wajch, Hausdorff compactifications in $${\\mathbf{Z}}{\\mathbf{F}}$$. Topology. Appl. 258, 79\u201399 (2019)","journal-title":"Topology. Appl."},{"key":"450_CR31","unstructured":"K. Kunen, Set Theory (An Introduction to Independence Proofs, North-Holland, Amsterdam, 1983)"},{"key":"450_CR32","volume-title":"The Foundations of Mathematics","author":"K Kunen","year":"2009","unstructured":"K. Kunen, The Foundations of Mathematics (Individual Authors and College Publications, London, 2009)"},{"key":"450_CR33","volume-title":"Handbook of Set-Theoretic Topology","year":"1984","unstructured":"K. Kunen, J.E. Vaughan (eds.), Handbook of Set-Theoretic Topology (North-Holland, Amsterdam, 1984)"},{"key":"450_CR34","doi-asserted-by":"crossref","unstructured":"H.-P. K\u00fcnzi, An Introduction to Quasi-Uniform Spaces, (in: F. Mynard and E. Pearl (Eds.), Beyond Topology, Contemporary Mathematics, vol. 486, Amer. Math. Soc., Providence, R.I., 2009, pp. 501\u2013566)","DOI":"10.1090\/conm\/486\/09511"},{"key":"450_CR35","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1080\/00029890.1965.11970596","volume":"72","author":"PA Loeb","year":"1965","unstructured":"P.A. Loeb, A new proof of the Tychonoff theorem. Am. Math. Monthly 72, 711\u2013717 (1965)","journal-title":"Am. Math. Monthly"},{"key":"450_CR36","first-page":"93","volume":"1","author":"J Nagata","year":"1950","unstructured":"J. Nagata, On a necessary and sufficient condition on metrizability. J. Inst. Polytech., Osaka City Univ. 1, 93\u2013100 (1950)","journal-title":"J. Inst. Polytech., Osaka City Univ."},{"issue":"2","key":"450_CR37","first-page":"6","volume":"3","author":"G Rano","year":"2013","unstructured":"G. Rano, T. Bag, Compact quasi-metric spaces. Int. J. Math. Sci. Comput. 3(2), 6\u20138 (2013)","journal-title":"Int. J. Math. Sci. Comput."},{"key":"450_CR38","first-page":"197","volume":"77","author":"YM Smirnov","year":"1951","unstructured":"Y.M. Smirnov, A necessary and sufficient condition for metrizability of a topological space. Dokl. Akad. Nauk. SSSR (N.S.) 77, 197\u2013200 (1951)","journal-title":"Dokl. Akad. Nauk. SSSR (N.S.)"},{"issue":"1","key":"450_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4064\/ba63-1-1","volume":"63","author":"E Tachtsis","year":"2015","unstructured":"E. Tachtsis, On the existence of free ultrafilters on $$ \\omega $$ and on Russell-sets in $${\\mathbf{Z}}{\\mathbf{F}}$$. Bull. Pol. Acad. Sci. Math. 63(1), 1\u201310 (2015)","journal-title":"Bull. Pol. Acad. Sci. Math."},{"key":"450_CR40","unstructured":"E. Tachtsis, Review of [42], Zbl 06893991"},{"key":"450_CR41","doi-asserted-by":"publisher","first-page":"106997","DOI":"10.1016\/j.topol.2019.106997","volume":"275","author":"E Tachtsis","year":"2020","unstructured":"E. Tachtsis, Infinite Hausdorff spaces may lack cellular or discrete subsets of cardinality $$\\aleph _0$$. Topology. Appl. 275, 106997 (2020)","journal-title":"Topology. Appl."},{"key":"450_CR42","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.topol.2018.03.031","volume":"241","author":"E Wajch","year":"2018","unstructured":"E. Wajch, Quasi-metrizability of products in $$\\mathbf{ ZF}$$ and equivalences of $${\\mathbf{CUT}}$$(fin). Topology. Appl. 241, 62\u201369 (2018)","journal-title":"Topology. Appl."},{"key":"450_CR43","volume-title":"General Topology, (Addison-Wesley Series in Math","author":"S Willard","year":"1970","unstructured":"S. Willard, General Topology, (Addison-Wesley Series in Math (Addison-Wesley Publishing Co., Reading, Massachusetts, 1970)"},{"key":"450_CR44","doi-asserted-by":"publisher","first-page":"675","DOI":"10.2307\/2371174","volume":"53","author":"WA Wilson","year":"1931","unstructured":"W.A. Wilson, On quasi-metric spaces. Am. J. Math. 53, 675\u2013684 (1931)","journal-title":"Am. J. Math."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-022-00450-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-022-00450-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-022-00450-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T14:00:50Z","timestamp":1669039250000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-022-00450-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,5]]},"references-count":44,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["450"],"URL":"https:\/\/doi.org\/10.1007\/s10998-022-00450-0","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,5]]},"assertion":[{"value":"25 February 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}