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Jordan curve theorems with respect to certain pretopologies on ℤ2

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2009) 5810 LNCS 252-262
DOI: 10.1007/978-3-642-04397-0_22
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Abstract

We discuss four quotient pretopologies of a certain basic topology on . Three of them are even topologies and include the well-known Khalimsky and Marcus-Wyse topologies. Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies. © 2009 Springer Berlin Heidelberg.

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Šlapal, J. (2009). Jordan curve theorems with respect to certain pretopologies on ℤ2. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5810 LNCS, pp. 252–262). https://doi.org/10.1007/978-3-642-04397-0_22

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