{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:25:05Z","timestamp":1761611105438,"version":"3.40.5"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Categorical Structures"],"published-print":{"date-parts":[[2003,2]]},"DOI":"10.1023\/a:1023017025800","type":"journal-article","created":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T22:17:24Z","timestamp":1049753844000},"page":"95-116","source":"Crossref","is-referenced-by-count":6,"title":["AFPP vs FPP"],"prefix":"10.1007","volume":"11","author":[{"given":"Michael B.","family":"Smyth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rueiher","family":"Tsaur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5120427_CR1","first-page":"1","volume-title":"Handbook of Logic in Computer Science","author":"S. Abramsky","year":"1994","unstructured":"Abramsky, S. and Jung, A.: Domain theory, in S. Abramsky, D. M. Gabbay and T. S. E. Maibaum (eds), Handbook of Logic in Computer Science, Vol. 3, Oxford University Press, Oxford, 1994, pp. 1\u2013168."},{"key":"5120427_CR2","unstructured":"Berge, C.: Espaces topologiques: functions multivoques, Dunod, Paris, 1959."},{"key":"5120427_CR3","volume-title":"Graphs and Hypergraphs","author":"C. Berge","year":"1973","unstructured":"Berge, C.: Graphs and Hypergraphs, North-Holland, Amsterdam, 1973."},{"key":"5120427_CR4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01196091","volume":"30","author":"C. Brink","year":"1993","unstructured":"Brink, C.: Power structures, Algebra Universalis\n30 (1993), 177\u2013216.","journal-title":"Algebra Universalis"},{"key":"5120427_CR5","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1215\/S0012-7094-54-02124-9","volume":"21","author":"C. Capel","year":"1954","unstructured":"Capel, C.: Inverse limit spaces, Duke Mathematical Journal\n21 (1954), 233\u2013246.","journal-title":"Duke Mathematical Journal"},{"key":"5120427_CR6","doi-asserted-by":"crossref","first-page":"2007","DOI":"10.1016\/S0031-3203(98)00065-X","volume":"31","author":"B. B. Chaudhuri","year":"1998","unstructured":"Chaudhuri, B. B. and Rosenfeld, A.: On the computation of the digital convex hull and circular hull of a digital region, Pattern Recognition\n31 (1998), 2007\u20132016.","journal-title":"Pattern Recognition"},{"key":"5120427_CR7","volume-title":"Introduction to Lattices and Order","author":"B. A. Davey","year":"1990","unstructured":"Davey, B. A. and Priestley, H. A.: Introduction to Lattices and Order, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1990."},{"key":"5120427_CR8","unstructured":"Giblin, P. J.: Graphs, Surfaces and Homology, Chapman and Hall, 1981."},{"key":"5120427_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/cm-48-1-1-5","volume":"48","author":"G. Gr\u00e4tzer","year":"1984","unstructured":"Gr\u00e4tzer, G. and Whitney, S.: Infinitary varieties of structures closed under the formation of complex structures, Colloquium Mathematicum\n48 (1984), 1\u20135.","journal-title":"Colloquium Mathematicum"},{"key":"5120427_CR10","doi-asserted-by":"crossref","unstructured":"Harary, F.: Graph Theory, Addison-Wesley, 1969.","DOI":"10.21236\/AD0705364"},{"key":"5120427_CR11","unstructured":"Hocking, J. G. and Young, G. S.: Topology, Addison-Wesley, 1961."},{"key":"5120427_CR12","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0012-365X(93)90568-E","volume":"120","author":"A. V. Ivashchenko","year":"1993","unstructured":"Ivashchenko, A. V.: The coordinate representation of a graph and n-universal graph of radius 1, Discrete Mathematics\n120 (1993), 107\u2013114.","journal-title":"Discrete Mathematics"},{"key":"5120427_CR13","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0012-365X(94)90261-5","volume":"126","author":"A. V. Ivashchenko","year":"1994","unstructured":"Ivashchenko, A. V.: Contractible transformations do not change the homology groups of graphs, Discrete Mathematics\n126 (1994), 159\u2013170.","journal-title":"Discrete Mathematics"},{"key":"5120427_CR14","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172066","volume-title":"Notes on Logic and Set Theory","author":"P. T. Johnstone","year":"1987","unstructured":"Johnstone, P. T.: Notes on Logic and Set Theory, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1987."},{"key":"5120427_CR15","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1109\/TPAMI.1981.4767162","volume":"3","author":"C. E. Kim","year":"1981","unstructured":"Kim, C. E.: On the cellular convexity of complexes, IEEE Transactions on Pattern Analysis Mach. Intell. (PAMI)\n3 (1981), 617\u2013625.","journal-title":"IEEE Transactions on Pattern Analysis Mach. Intell. (PAMI)"},{"key":"5120427_CR16","doi-asserted-by":"crossref","unstructured":"Lawson, J. D.: The versatile continuous order, in M. Main, A. Melton, M. Mislove and D. Schmidt (eds), Mathematical Foundations of Programming Language Semantics (MFPLS 1987), Lecture Notes in Computer Science 298, Springer-Verlag, 1987, pp. 134\u2013160.","DOI":"10.1007\/3-540-19020-1_7"},{"key":"5120427_CR17","volume-title":"Continuum Theory","author":"S. Nadler","year":"1992","unstructured":"Nadler, S.: Continuum Theory, Marcel Dekker, New York, 1992."},{"key":"5120427_CR18","unstructured":"Poston, T.: Fuzzy geometry, Ph.D. Thesis, University of Warwick, 1971."},{"key":"5120427_CR19","first-page":"121","volume":"4","author":"A. Pultr","year":"1963","unstructured":"Pultr, A.: An analogon of the fixed-point theorem and its application for graphs, Commentationes Mathematicae Universitatis Carolinae\n4 (1963), 121\u2013131.","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"5120427_CR20","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0167-8655(86)90017-6","volume":"4","author":"A. Rosenfeld","year":"1986","unstructured":"Rosenfeld, A.: \u2018Continuous\u2019 functions on digital pictures, Pattern Recognition Letters\n4 (1986), 177\u2013184.","journal-title":"Pattern Recognition Letters"},{"key":"5120427_CR21","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1090\/S0002-9939-1971-0274349-1","volume":"28","author":"R. E. Smithson","year":"1971","unstructured":"Smithson, R. E.: Fixed points of order preserving multifunctions, Proceedings of the American Mathematical Society\n28 (1971), 304\u2013310.","journal-title":"Proceedings of the American Mathematical Society"},{"key":"5120427_CR22","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/oso\/9780198537359.003.0005","volume-title":"Handbook of Logic in Computer Science","author":"M. B. Smyth","year":"1992","unstructured":"Smyth, M. B.: Topology, in S. Abramsky, D. M. Gabbay and T. S. E. Maibaum (eds), Handbook of Logic in Computer Science, Vol. 1, Oxford University Press, Oxford, 1992, pp. 641\u2013761."},{"key":"5120427_CR23","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/0304-3975(95)00053-Y","volume":"151","author":"M. B. Smyth","year":"1995","unstructured":"Smyth, M. B.: Semi-metrics, closure spaces and digital topology, Theoretical Computer Science\n151 (1995), 257\u2013276.","journal-title":"Theoretical Computer Science"},{"key":"5120427_CR24","unstructured":"Smyth, M. B.: Inverse limits of graphs, in C. Hankin, I. Mackie and R. Nagarajan (eds), Theory and Formal Methods 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods, Imperial College Press, 1995."},{"key":"5120427_CR25","unstructured":"Smyth, M. B. and Webster, J.: Finite approximation of functions using inverse sequences of graphs, in A. Edalat, S. Jourdan and G. McCusker (eds), Advances in Theory and Formal Methods in Computing: Proceedings of the Third Imperial College Workshop, Imperial College Press, 1996."},{"key":"5120427_CR26","doi-asserted-by":"crossref","unstructured":"Smyth, M. B.: Lines as topological graphs, in S. Andima, R. C. Flagg, G. Itzkowitz, Y. Kong, R. Kopperman and P. Misra (eds), Papers on General Topology and Applications: Eleventh Summer Conference at the University of Southern Maine, Annals of the New York Academy of Science 806, New York Academy of Sciences, 1996, pp. 413\u2013432.","DOI":"10.1111\/j.1749-6632.1996.tb49184.x"},{"key":"5120427_CR27","unstructured":"Smyth, M. B.: Topology and tolerance, in S. Brookes and M. Mislove (eds), MFPS XIII Mathematical Foundations of Programming Semantics, Thirteenth Annual Conference, Electronic Notes in Theoretical Computer Science 6, Elsevier Science B. V., 1997, http:\/\/ www.elsevier.nl\/locate\/entcs\/volume6.html."},{"key":"5120427_CR28","unstructured":"Tsaur, R. and Smyth, M. B.: Convexity and almost fixed point properties in graphs: A study of many-valued functions in Helly and dismantlable graphs, submitted for publication."},{"key":"5120427_CR29","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/0012-365X(84)90188-2","volume":"48","author":"J. W. Walker","year":"1984","unstructured":"Walker, J. W.: Isotone relations and the fixed point property for posets, Discrete Mathematics\n48 (1984), 275\u2013288.","journal-title":"Discrete Mathematics"},{"key":"5120427_CR30","unstructured":"Webster, J.: Continuum theory in the digital setting, in K. P. Hart, E. Pearl and P. Simon (eds), Electronic Proceedings of the Eighth Prague Topological Symposium, Topology Atlas, 1996, pp. 371\u2013386, http:\/\/at.yorku.ca\/p\/p\/a\/c\/09.htm."},{"key":"5120427_CR31","unstructured":"Webster, J.: Topology and measure theory in the digital setting: On the approximation of spaces by inverse sequences of graphs, Ph.D. Thesis, Imperial College, 1997."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023017025800.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1023017025800\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1023017025800.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T14:33:49Z","timestamp":1747578829000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1023017025800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,2]]}},"alternative-id":["5120427"],"URL":"https:\/\/doi.org\/10.1023\/a:1023017025800","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"type":"print","value":"0927-2852"},{"type":"electronic","value":"1572-9095"}],"subject":[],"published":{"date-parts":[[2003,2]]}}}