Abstract:ABSTRACT. The properties of the collection of complements of @-closures of sets in a topological space are investigated in %his paper. A strong continuity condition is defined in terms of these sets. Some applications to H-closed spaces and Katetov spaces are given.
“…In this section, we strengthen this result by replacing both the θ-g-closed and continuous requirements with weaker conditions. Our replacement for the θ-g-closed condition uses the concept of a θ-c-open set from [2].…”
Section: Sufficient Conditions For Images Of θ-G-closed Sets To Be θ-mentioning
confidence: 99%
“…The purpose of this note is to strengthen slightly some of the results in [5] concerning the preservation of θ-generalized closed sets. This is done by using the notion of a θ-c-closed set developed by Baker [2]. These sets turn out to be a very natural tool to use in investigating the preservation of θ-generalized closed sets.…”
Section: Introduction Recently Dontchev and Makimentioning
Abstract. The purpose of this note is to strengthen several results in the literature concerning the preservation of θ-generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets are θ-generalized closed. In this process several new weak forms of continuous functions and closed functions are developed.
“…In this section, we strengthen this result by replacing both the θ-g-closed and continuous requirements with weaker conditions. Our replacement for the θ-g-closed condition uses the concept of a θ-c-open set from [2].…”
Section: Sufficient Conditions For Images Of θ-G-closed Sets To Be θ-mentioning
confidence: 99%
“…The purpose of this note is to strengthen slightly some of the results in [5] concerning the preservation of θ-generalized closed sets. This is done by using the notion of a θ-c-closed set developed by Baker [2]. These sets turn out to be a very natural tool to use in investigating the preservation of θ-generalized closed sets.…”
Section: Introduction Recently Dontchev and Makimentioning
Abstract. The purpose of this note is to strengthen several results in the literature concerning the preservation of θ-generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets are θ-generalized closed. In this process several new weak forms of continuous functions and closed functions are developed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.