Open AccessSeparability of path spaces under the open-point and bi-point-open topologies
Author(s) -
Aashi 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.