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Particular Point Topology
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Details
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The particular point topology is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. A generalization of the particular point topology is the closed extension topology. In the case when X {p} has the discrete topology, the closed extension topology is the same as the particular point topology. This topology is used to provide interesting examples and counterexamples. Since every nonempty open set contains p, no nonempty closed sets can be separated by neighbourhoods from each other, and thus X is not normal. Exception: the Sierpinski topology is normal, and even completely normal, since it contains no nontrivial separated sets.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131261268
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131261268
- Format Fachbuch
- Titel Particular Point Topology
- Herausgeber Betascript Publishing
- Anzahl Seiten 104
- Genre Mathematik
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