Semiregular Property on Generalized Compact and Paracompact Spaces

Abstract

Misalkan $(X, \tau)$ ruang topologi dan $(X, \tau^\ast)$ semiregularannya. Maka sifat topologi ${\cal P}$ adalah semiregularan asalkan $\tau$ mempunyai sifat ${\cal P}$ jika dan hanya jika $\tau^\ast$ mempunyai sifat yang serupa. Dalam kertas ini, kami menyelidiki sifat semiregularan di atas beberapa ruang padat dan para--padat teritlak, iaitu ruang para-padat, hampir padat, padat lemah dan para--padat lemah. Katakunci: Semiregularan; sifat semiregularan; ruang padat dan ruang para-padat. We let $(X, \tau)$ be a topological space and $(X, \tau^{\ast})$ its semiregularization. Then a topological property ${\cal P}$ is semiregular provided that $\tau$ has property ${\cal P}$ if and only if $\tau^{\ast}$ has the same property. In this work, we study semiregular property on some generalizations of compact and paracompact spaces; namely, paracompact, nearly paracompact, weakly compact and weakly paracompact spaces. Keywords: Semiregularity; semiregular property; compact and paracompact spaces.