Quasihomeomorphisms and Some Topological Properties

Abstract

In this paper, we study the properties of topological spaces preserved by quasihomeomorphisms. Particularly, we show that quasihomeomorphisms preserve Whyburn, weakly Whyburn, submaximal and door properties. Moreover, we offer necessary conditions on continuous map q:X→Y where Y is Whyburn (resp., weakly Whyburn ) in order to render X Whyburn (resp., weakly Whyburn). Also, we prove that if q:X→Y is a one-to-one continuous map and Y is submaximal (resp., door), then X is submaximal (resp., door). Finally, we close this paper by studying the relation between quasihomeomorphisms and k-primal spaces.

Keywords

• quasihomeomorphism
• Alexandroff space
• Whyburn space
• submaximal space
• primal space
• factorisation systems