Topologies associated with the one point compactifications of Khalimsky topological spaces
| Autor: | Sang-Eon Han, Il-Kang Na |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Alexandroff extension Nowhere dense set 010102 general mathematics Structure (category theory) Excluded point topology Topological space Space (mathematics) 01 natural sciences 010101 applied mathematics Geometry and Topology 0101 mathematics Particular point topology Quotient Mathematics |
| Zdroj: | Topology and its Applications. 241:333-344 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2018.03.036 |
| Popis: | In this paper, after discussing the one point compactification of the Khalimsky line (resp. the Khalimsky plane), denoted by ( Z ⁎ , κ ⁎ ) (resp. ( ( Z 2 ) ⁎ , ( κ 2 ) ⁎ ) ), we study various properties of these compactifications associated with the semi- T 1 2 axiom, a non-Alexandroff structure, a non-cut-point space and so forth. We also investigate dense subsets and nowhere dense subsets of ( Z ⁎ , κ ⁎ ) and ( ( Z 2 ) ⁎ , ( κ 2 ) ⁎ ) . Finally, motivated by a particular point topology and an excluded point topology, we develop two kinds of new topologies as quotient topological spaces of ( Z ⁎ , κ ⁎ ) called an excluded two points topology and a cofinite particular point topology. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect