Separability of path spaces under the open-point and bi-point-open topologies | Zendy

Anubha Jindal | Zendy

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Separability of path spaces under the open-point and bi-point-open topologies

Author(s) -

Anubha Jindal

Publication year - 2021

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2107209j

Subject(s) - mathematics , open set , network topology , tychonoff space , topology (electrical circuits) , point (geometry) , hausdorff space , compact open topology , space (punctuation) , open and closed maps , general topology , topological space , discrete mathematics , combinatorics , computer science , geometry , topological tensor product , biochemistry , chemistry , functional analysis , gene , operating system

In [3], two new kinds of topologies called the open-point topology and the bi-point-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X, have been introduced. In this article, we study the separability of the space P(X), of all continuous maps on [0; 1] into a Hausdorff space X, with the open-point and bi-point-open topologies. Our result also demonstrates, the claim made in [3], that both the domain as well as the codomain play significant roles in the construction of the open-point and bi-point-open topologies.

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