Discrete generators
type: Item
instance of: scholarly article
title: Discrete generators
zbMATH Open document ID: 1499.54085
author: Ziqin Feng
author: Paul Gartside
author: Alex Yuschik
published in: Acta Mathematica Hungarica
publication date: 2022-03-16T00:00:00Z
review text: A subset \(G\) of the space \(C(X)\) of all real continuous functions defined on a topological space \(X\) is called a generator if for each point \(x\) belonging to the exterior of some closed set \(C\) of \(X\) there exists a function \(g\) in \(G\) such that \(g(x)\) is in the exterior of image \(g(C)\). Every generator is considered as a topological subspace of \(C(X)\) endowed with the topology of pointwise convergence. Spaces possesing a discrete generator are characterised, mainly in terms of cardinal invariants. Interesting counterexamples are constructed and open conjectures are formulated as further problems in this area. This paper is a continuation of earlier investigations of authors, concerning spaces with a compact generators and spaces with a first or second countable generators.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 7491532
zbMATH Keywords: space of continuous functions
zbMATH Keywords: compact-open topology
zbMATH Keywords: pointwise topology
zbMATH Keywords: Tychonoff space
zbMATH Keywords: discrete generator
zbMATH Keywords: zero-dimensional space
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
full work available at URL: s10474-022-01207-4
OpenAlex ID: W4210827895
cites work: Q3779415
cites work: A note on separating function sets
cites work: Q4150804
cites work: First and second countable generators
cites work: Two More Hereditarily Separable Non-Lindelöf Spaces
cites work: A relation between perfect separability, completeness, and normality in semi-metric spaces
cites work: Partition Problems in Topology
cites work: Colouring and non-productivity of \(\aleph_ 2\)-c.c
cites work: Hereditary m-separability and the hereditary m-Lindelöf property in product spaces and function spaces
DOI: 10.1007/S10474-022-01207-4
description: scientific article; zbMATH DE number 7491532