{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:34:36Z","timestamp":1759638876269},"publisher-location":"Cham","reference-count":28,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319276823"},{"type":"electronic","value":"9783319276830"}],"license":[{"start":{"date-parts":[[2015,12,10]],"date-time":"2015-12-10T00:00:00Z","timestamp":1449705600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-27683-0_21","type":"book-chapter","created":{"date-parts":[[2015,12,9]],"date-time":"2015-12-09T21:16:29Z","timestamp":1449695789000},"page":"299-316","source":"Crossref","is-referenced-by-count":6,"title":["The Urysohn Extension Theorem for Bishop Spaces"],"prefix":"10.1007","author":[{"given":"Iosif","family":"Petrakis","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,12,10]]},"reference":[{"key":"21_CR1","volume-title":"Foundations of Constructive Analysis","author":"E Bishop","year":"1967","unstructured":"Bishop, E.: Foundations of Constructive Analysis. McGraw-Hill, New York (1967)"},{"key":"21_CR2","first-page":"53","volume-title":"Intuitionism and Proof Theory","author":"E Bishop","year":"1970","unstructured":"Bishop, E.: Mathematics as a numerical language. In: Kino, A., Myhill, J., Vesley, R.E. (eds.) Intuitionism and Proof Theory, pp. 53\u201371. North-Holland, Amsterdam (1970)"},{"key":"21_CR3","doi-asserted-by":"crossref","unstructured":"Bishop, E., Cheng, H.: Constructive measure theory. Mem. Amer. Math. Soc. 116 (1972)","DOI":"10.1090\/memo\/0116"},{"key":"21_CR4","series-title":"Grundlehren der mathematischen Wissenschaften","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61667-9","volume-title":"Constructive Analysis","author":"Errett Bishop","year":"1985","unstructured":"Bishop, E., Bridges, D.: Constructive Analysis, Grundlehren der Math. Wissenschaften 279. Springer, Heidelberg (1985)"},{"key":"21_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565663","volume-title":"Varieties of Constructive Mathematics","author":"DS Bridges","year":"1987","unstructured":"Bridges, D.S., Richman, F.: Varieties of Constructive Mathematics. Cambridge University Press, Cambridge (1987)"},{"key":"21_CR6","series-title":"CiE Series Theory and Applications of Computability","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22415-7","volume-title":"Apartness and Uniformity: A Constructive Development","author":"D Bridges","year":"2011","unstructured":"Bridges, D., V\u00ee\u0163\u0103, L.S.: Apartness and Uniformity: A Constructive Development. CiE Series Theory and Applications of Computability. Springer, Heidelberg (2011)"},{"key":"21_CR7","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.apal.2011.06.018","volume":"163","author":"D Bridges","year":"2012","unstructured":"Bridges, D.: Reflections on function spaces. Ann. Pure Appl. Logic 163, 101\u2013110 (2012)","journal-title":"Ann. Pure Appl. Logic"},{"key":"21_CR8","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF01209181","volume":"96","author":"LEJ Brouwer","year":"1926","unstructured":"Brouwer, L.E.J.: Zur Begr\u00fcndung der intuitionistische Mathematik III. Math. Ann. 96, 451\u2013488 (1926)","journal-title":"Math. Ann."},{"key":"21_CR9","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0091894","volume-title":"Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretic Studies","author":"W Buchholz","year":"1981","unstructured":"Buchholz, W., Feferman, S., Pohlers, W., Sieg, W.: Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretic Studies. LNM, vol. 897. Springer, Heidelberg (1981)"},{"key":"21_CR10","volume-title":"Topology","author":"J Dugundji","year":"1989","unstructured":"Dugundji, J.: Topology. Wm. C. Brown Publishers, Dubuque (1989)"},{"key":"21_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7819-2","volume-title":"Rings of Continuous Functions","author":"L Gillman","year":"1960","unstructured":"Gillman, L., Jerison, M.: Rings of Continuous Functions. Van Nostrand, Princeton (1960)"},{"key":"21_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0003-4843(81)90010-3","volume":"20","author":"RJ Grayson","year":"1981","unstructured":"Grayson, R.J.: Concepts of general topology in constructive mathematics and in sheaves. Ann. Math. Logic 20, 1\u201341 (1981)","journal-title":"Ann. Math. Logic"},{"key":"21_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF03018603","volume":"22","author":"M Fr\u00e9chet","year":"1906","unstructured":"Fr\u00e9chet, M.: Sur quelques points du calcul fonctionnel. Rend. Circ. Mat. di Palermo 22, 1\u201374 (1906)","journal-title":"Rend. Circ. Mat. di Palermo"},{"key":"21_CR14","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.apal.2006.01.004","volume":"141","author":"H Ishihara","year":"2006","unstructured":"Ishihara, H., Mines, R., Schuster, P., V\u00ee\u0163\u0103, L.S.: Quasi-apartness and neighborhood spaces. Ann. Pure Appl. Logic 141, 296\u2013306 (2006)","journal-title":"Ann. Pure Appl. Logic"},{"key":"21_CR15","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.apal.2011.06.022","volume":"163","author":"H Ishihara","year":"2013","unstructured":"Ishihara, H.: Two subcategories of apartness spaces. Ann. Pure Appl. Logic 163, 132\u2013139 (2013)","journal-title":"Ann. Pure Appl. Logic"},{"key":"21_CR16","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1016\/j.apal.2012.10.009","volume":"164","author":"H Ishihara","year":"2013","unstructured":"Ishihara, H.: Relating Bishop\u2019s function spaces to neighborhood spaces. Ann. Pure Appl. Logic 164, 482\u2013490 (2013)","journal-title":"Ann. Pure Appl. Logic"},{"key":"21_CR17","volume-title":"Notes on Constructive Mathematics","author":"P Martin-L\u00f6f","year":"1968","unstructured":"Martin-L\u00f6f, P.: Notes on Constructive Mathematics. Almqvist and Wiksell, Stockholm (1968)"},{"key":"21_CR18","volume-title":"Intuitionistic Type Theory: Notes by Giovanni Sambin on a Series of Lectures Given in Padua, June 1980","author":"P Martin-L\u00f6f","year":"1984","unstructured":"Martin-L\u00f6f, P.: Intuitionistic Type Theory: Notes by Giovanni Sambin on a Series of Lectures Given in Padua, June 1980. Bibliopolis, Napoli (1984)"},{"key":"21_CR19","unstructured":"Martino, E., Giaretta, P.: Brouwer Dummett, and the bar theorem. In: Bernini, S. (ed.) Atti del Congresso Nazionale di Logica, Montecatini Terme, 1\u20135 Ottobre 1979, Napoli, pp. 541\u2013558 (1981)"},{"key":"21_CR20","doi-asserted-by":"publisher","first-page":"347","DOI":"10.2307\/2272159","volume":"40","author":"J Myhill","year":"1975","unstructured":"Myhill, J.: Constructive set theory. J. Symbolic Logic 40, 347\u2013382 (1975)","journal-title":"J. Symbolic Logic"},{"key":"21_CR21","series-title":"Synthese Library","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/978-1-4020-8926-8_12","volume-title":"Logicism, Intuitionism, and Formalism","author":"E Palmgren","year":"2009","unstructured":"Palmgren, E.: From intuitionistic to point-free topology: on the foundations of homotopy theory. In: Lindstr\u00f6m, S., et al. (eds.) Logicism, Intuitionism, and Formalism. Synthese Library, vol. 341, pp. 237\u2013253. Springer, Heidelberg (2009)"},{"key":"21_CR22","unstructured":"Petrakis, I.: Bishop spaces: constructive point-function topology, In: Mathematisches Forschungsinstitut Oberwolfach Report No. 52\/2014, Mathematical Logic: Proof Theory, Constructive Mathematics, pp. 26\u201327 (2014)"},{"key":"21_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-3-319-20028-6_31","volume-title":"Evolving Computability","author":"I Petrakis","year":"2015","unstructured":"Petrakis, I.: Completely regular bishop spaces. In: Beckmann, A., Mitrana, V., Soskova, M. (eds.) CiE 2015. LNCS, vol. 9136, pp. 302\u2013312. Springer, Heidelberg (2015)"},{"key":"21_CR24","unstructured":"Petrakis, I.: Constructive topology of Bishop spaces. Ph.D. thesis, LMU Munich (2015)"},{"key":"21_CR25","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/978-1-4613-0897-3_12","volume-title":"Mathematical Logic and its Applications","author":"G Sambin","year":"1987","unstructured":"Sambin, G.: Intuitionistic formal spaces - a first communication. In: Skordev, D. (ed.) Mathematical Logic and its Applications, pp. 187\u2013204. Plenum Press, New York (1987)"},{"key":"21_CR26","unstructured":"Sambin, G.: The Basic Picture: Structures for Constructive Topology. Oxford University Press (in press)"},{"issue":"1","key":"21_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1215\/S0012-7094-63-03001-1","volume":"30","author":"E Spanier","year":"1963","unstructured":"Spanier, E.: Quasi-topologies. Duke Math. J. 30(1), 1\u201314 (1963)","journal-title":"Duke Math. J."},{"key":"21_CR28","unstructured":"Troelstra, A.S.: Intuitionistic general topology. Ph.D. thesis, Amsterdam (1966)"}],"container-title":["Lecture Notes in Computer Science","Logical Foundations of Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-27683-0_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T21:31:40Z","timestamp":1559338300000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-27683-0_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,10]]},"ISBN":["9783319276823","9783319276830"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-27683-0_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015,12,10]]}}}