The open-point and bi-point-open topologies on \(C(X)\): submetrizability and cardinal functions
type: Item
instance of: scholarly article
title: The open-point and bi-point-open topologies on \(C(X)\): submetrizability and cardinal functions
zbMATH Open document ID: 1331.54019
author: Anubha Jindal
author: R. A. McCoy
author: S. Kundu
published in: Topology and its Applications
publication date: 2015-11-16T00:00:00Z
review text: Denote by \(C_h(X)\) (resp. \(C_{ph}(X)\)) the \textit{open-point } (resp. \textit{bi-point-open}) topology on the space \(C(X)\) of all real-valued continuous functions on a Tychonoff space \(X\), which have subbase elements of the form \[ \{ f\in C(X): f^{-1}(r)\cap U\neq\emptyset\}, \] where \(U\) is \(X\)-open, and \(r\in \mathbb R\) (resp. \[ \{ f\in C(X): f^{-1}(r)\cap U\neq\emptyset \;\text{and} \;f(x)\in V\}, \] where \(U\) is \(X\)-open, \(x\in X\), \(V\) is \(\mathbb R\)-open, and \(r\in \mathbb R\)). The authors study submetrizability, as well as various cardinal functions, such as extent, cellularity, weight, pseudocharacter, character and tightness, for the spaces \(C_h(X),C_{ph}(X)\).
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54E99
zbMATH DE Number: 6509446
zbMATH Keywords: point-open topology
zbMATH Keywords: open-point topology
zbMATH Keywords: bi-point-open topology
zbMATH Keywords: induced map
zbMATH Keywords: restriction map
zbMATH Keywords: sum function
zbMATH Keywords: \(G_\delta\)-set
zbMATH Keywords: submetrizability
zbMATH Keywords: cardinal functions
zbMATH Keywords: extent
zbMATH Keywords: cellularity
zbMATH Keywords: weight
zbMATH Keywords: pseudocharacter
zbMATH Keywords: character
zbMATH Keywords: tightness
reviewed by: Laszlo Zsilinszky
MaRDI profile type: Publication
full work available at URL: j.topol.2015.09.042
OpenAlex ID: W2180114633
cites work: A topology for spaces of transformations
cites work: Topologies for function spaces
cites work: Q4002497
cites work: Q3994935
cites work: On topologies for function spaces
cites work: The compact-\(G_\delta\)-open topology on \(C(X)\)
cites work: Q3218783
cites work: Comparison of Topologies on Function Spaces
cites work: The open-point and bi-point-open topologies on \(C(X)\)
cites work: Topological properties of spaces of continuous functions
cites work: Q5613067
cites work: A \(C_p\)-theory problem book. Topological and function spaces
cites work: A \(C_p\)-theory problem book. Special features of function spaces
cites work: A \(C_p\)-theory problem book. Compactness in function spaces
DOI: 10.1016/J.TOPOL.2015.09.042
description: scientific article; zbMATH DE number 6509446