Open Extension Topology

Authors

  • Вячеслав Бабич Taras Shevchenko National University of Kyiv, Ukraine
  • Василий Пехтерев Taras Shevchenko National University of Kyiv, Ukraine

DOI:

https://doi.org/10.15673/2072-9812.2/2015.51570

Keywords:

Topological space, base, connectedness, separation axioms, cardinal invariants.

Abstract

The paper contains the results which describe the properties of such general topological construction as open extension topology. In particular, we prove that this topology is not transitive. We find the base of the least cardinality for the topology and local one for the neighborhood system of every point. We calculate the interior, the closure, and the sets of isolated and limit points of any set. Also we prove that this space is path connected and is not metrizable, and investigate its cardinal invariants and separation axioms.

References

Lynn Arthur Steen and J. Arthur Seebach, Jr. Counterexamples in topology. -- New York: Dover publications, 1978. -- 256 p.

Бабич В. М., Філоненко О. М. Топологія розширення // Наук. вісник Ужгород. ун-ту. -- 2015. -- 27-1. -- С. 5-9.

Энгелькинг Р. Общая топология. -- М.: Мир, 1986. -- 750 с.

Published

2015-10-15