Strongly δcl-continuous functions in topological spaces

Subject Areas :

Masoumeh Etebar ¹

1 - Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Received: 2022-04-13 Accepted : 2022-07-09 Published : 2024-01-18

Keywords: cl-کاملاً منظم, فضای &delta, cl- باز, فضای &delta, cl- فشرده, فضای s- نسبتاًپیرافشرده, cl- منظم, فضای &delta, مجموعه‌ی &delta,

Abstract :

A new continuity between topological spaces, namely strongly δcl-continuity, is introduced and studied. Basic properties of strongly δcl -continuous functions are investigated. It is proved that for a weakly locally connected space X the strong δcl-continuity of a function f from X into Y is equivalent to the δcl-supercontinuity of f . Using this fact and studying the behavior of strongly δcl-continuous functions on the quasi-components of their domains it is observed that for every weakly locally connected space X there exists a discrete space Y such that the ring of all real-valued strongly δcl-continuous functions is isomorphic to C(Y) . Introducing and using s-regular open sets in a space new separation axioms such as δcl T1, δcl T2, δcl-regular and δcl-complete regularity of the space are created and the relations of these axioms with strongly δcl-continuous functions are investigated. Among them, it is proved that if X is a δcl-completely regular space and f is a δcl-homeomorphism, then X and Y are homeomorphic completely regular spaces. New topological properties; δcl -compactness and s- nearly paracompactness, their properties and relations with strongly δcl-continuous functions are studied. It is observed that if Y is open in X and A is δcl-compact in Y , then A is δcl-compact in X . Furthermore, the image of a δcl-compact space under a strongly δcl-continuous function is compact. Finally the properties of graphs of strongly δcl -continuous functions and δcl-quotient spaces are studied.

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