{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T13:15:11Z","timestamp":1725887711360},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319591070"},{"type":"electronic","value":"9783319591087"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"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":[[2017]]},"DOI":"10.1007\/978-3-319-59108-7_11","type":"book-chapter","created":{"date-parts":[[2017,5,16]],"date-time":"2017-05-16T04:43:06Z","timestamp":1494909786000},"page":"132-141","source":"Crossref","is-referenced-by-count":0,"title":["A Relational Generalization of the Khalimsky Topology"],"prefix":"10.1007","author":[{"given":"Josef","family":"\u0160lapal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,17]]},"reference":[{"key":"11_CR1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TPAMI.2007.70725","volume":"30","author":"VE Brimkov","year":"2008","unstructured":"Brimkov, V.E., Klette, R.: Border and surface tracing - theoretical foundations. IEEE Trans. Pattern Anal. Mach. Intell. 30, 577\u2013590 (2008)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"11_CR2","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph Theory","author":"JA Bondy","year":"2008","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory. Graduate Texts in Mathematics. Springer, Heidelberg (2008)"},{"key":"11_CR3","volume-title":"General Topology","author":"R Engelking","year":"1977","unstructured":"Engelking, R.: General Topology. Pa\u0144stwowe Wydawnictwo Naukowe, Warszawa (1977)"},{"key":"11_CR4","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.2298\/FIL1206101K","volume":"26","author":"S-E Han","year":"2012","unstructured":"Han, S.-E.: Compression of Khalimsky topological spaces. Filomat 26, 1101\u20131114 (2012)","journal-title":"Filomat"},{"key":"11_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0166-8641(90)90031-V","volume":"36","author":"ED Khalimsky","year":"1990","unstructured":"Khalimsky, E.D., Kopperman, R., Meyer, P.R.: Computer graphics and connected topologies on finite ordered sets. Topology Appl. 36, 1\u201317 (1990)","journal-title":"Topology Appl."},{"key":"11_CR6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1155\/S1048953390000041","volume":"3","author":"ED Khalimsky","year":"1990","unstructured":"Khalimsky, E.D., Kopperman, R., Meyer, P.R.: Boundaries in digital plane. J. Appl. Math. Stochast. Anal. 3, 27\u201355 (1990)","journal-title":"J. Appl. Math. Stochast. Anal."},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/3-540-44438-6_5","volume-title":"Discrete Geometry for Computer Imagery","author":"CO Kiselman","year":"2000","unstructured":"Kiselman, C.O.: Digital Jordan curve theorems. In: Borgefors, G., Nystr\u00f6m, I., Baja, G.S. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 46\u201356. Springer, Heidelberg (2000). doi:\n10.1007\/3-540-44438-6_5"},{"key":"11_CR8","first-page":"902","volume":"98","author":"TY Kong","year":"1991","unstructured":"Kong, T.Y., Kopperman, R., Meyer, P.R.: A topological approach to digital topology. Am. Math. Monthly 98, 902\u2013917 (1991)","journal-title":"Am. Math. Monthly"},{"key":"11_CR9","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0734-189X(85)80070-0","volume":"32","author":"TY Kong","year":"1985","unstructured":"Kong, T.Y., Roscoe, W.: A theory of binary digital pictures. Comput. Vision Graphics Image Process. 32, 221\u2013243 (1985)","journal-title":"Comput. Vision Graphics Image Process."},{"key":"11_CR10","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0734-189X(89)90147-3","volume":"48","author":"TY Kong","year":"1989","unstructured":"Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48, 357\u2013393 (1989)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"11_CR11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02574681","volume":"6","author":"R Kopperman","year":"1991","unstructured":"Kopperman, R., Meyer, P.R., Wilson, R.G.: A Jordan surface theorem for three-dimensional digital space. Discr. Comput. Geom. 6, 155\u2013161 (1991)","journal-title":"Discr. Comput. Geom."},{"key":"11_CR12","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s10851-007-0006-9","volume":"28","author":"E Melin","year":"2007","unstructured":"Melin, E.: Digital surfaces and boundaries in Khalimsky spaces. J. Math. Imaging and Vision 28, 169\u2013177 (2007)","journal-title":"J. Math. Imaging and Vision"},{"key":"11_CR13","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.jat.2007.06.003","volume":"150","author":"E Melin","year":"2008","unstructured":"Melin, E.: Continuous digitization in Khalimsky spaces. J. Approx. Theory 150, 96\u2013116 (2008)","journal-title":"J. Approx. Theory"},{"key":"11_CR14","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1145\/321556.321570","volume":"17","author":"A Rosenfeld","year":"1970","unstructured":"Rosenfeld, A.: Connectivity in digital pictures. J. Assoc. Comput. Math. 17, 146\u2013160 (1970)","journal-title":"J. Assoc. Comput. Math."},{"key":"11_CR15","doi-asserted-by":"crossref","first-page":"621","DOI":"10.2307\/2321290","volume":"86","author":"A Rosenfeld","year":"1979","unstructured":"Rosenfeld, A.: Digital topology. Amer. Math. Monthly 86, 621\u2013630 (1979)","journal-title":"Amer. Math. Monthly"},{"key":"11_CR16","first-page":"39","volume":"18","author":"J \u0160lapal","year":"1991","unstructured":"\u0160lapal, J.: Cardinal arithmetics of general relational systems. Publ. Math. Debrecen 18, 39\u201348 (1991)","journal-title":"Publ. Math. Debrecen"},{"key":"11_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/978-3-642-10210-3_33","volume-title":"Combinatorial Image Analysis","author":"J \u0160lapal","year":"2009","unstructured":"\u0160lapal, J.: Convenient closure operators on \n            $$\\mathbb{Z}^2$$\n          . In: Wiederhold, P., Barneva, R.P. (eds.) IWCIA 2009. LNCS, vol. 5852, pp. 425\u2013436. Springer, Heidelberg (2009). doi:\n10.1007\/978-3-642-10210-3_33"},{"key":"11_CR18","first-page":"425","volume":"15","author":"J \u0160lapal","year":"2013","unstructured":"\u0160lapal, J.: Topological structuring of the digital plane. Discr. Math. Theor. Comput. Sci. 15, 425\u2013436 (2013)","journal-title":"Discr. Math. Theor. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Combinatorial Image Analysis"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-59108-7_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,5,16]],"date-time":"2017-05-16T04:46:42Z","timestamp":1494910002000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-59108-7_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319591070","9783319591087"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-59108-7_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}