A New Topology Via a Topology

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American Institute of Physics Inc.
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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. © 2022 American Institute of Physics Inc.. All rights reserved.
Continuity, Open Set, Topological Space
Dagci, F. I., & Cakalli, H. (2022, November). A new topology via a topology. In AIP Conference Proceedings (Vol. 2483, No. 1, p. 020003). AIP Publishing LLC.