A New Topology Via a Topology

Dagci F. I., Cakalli H.

5th International Conference of Mathematical Sciences, ICMS 2021, İstanbul, Turkey, 23 - 27 June 2021, vol.2483 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2483
  • Doi Number: 10.1063/5.0115543
  • City: İstanbul
  • Country: Turkey
  • Keywords: continuity, open set, topological space
  • Istanbul Kültür University Affiliated: Yes

Abstract

In this extended abstract, we modify the definition of h-open set introduced in [1] by F. Abbas who neglects that the set of all h-open sets is a topology, and we show that the union of any family of h-open subsets of X is h-open that ensures that the set of all h-open subsets of a topological space (X, τ) forms a topology which is finer than τ, where a subset A of a topological space (X, τ) is said to be h-open if A ⊆ Int(A ∪ U) for every non-empty subset U of X such that U ∈ τ. We also give continuity type theorems.