Precalibers, monolithic spaces, first countability, and homogeneity in the class of compact spaces
type: Item
instance of: scholarly article
title: Precalibers, monolithic spaces, first countability, and homogeneity in the class of compact spaces
zbMATH Open document ID: 1155.54005
published in: Topology and its Applications
publication date: 2008-11-12T00:00:00Z
review text: The importance of some cardinal invariants in compact spaces is studied. A compact \(T_2\)-space \(X\) is either separable or can be continuously mapped onto a compact space of weight \(\omega_1\) which has a dense non-separable subspace. A strong form of homogeneity, called shell-homogeneity, is introduced and studied. For example: a shell-homogeneous monolithic compactum is first countable; for any first countable zero-dimensional space \(X\), the space \(X^{\omega}\) is shell-homogeneous. Several open problems are formulated.
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54D65
zbMATH DE Number: 5365227
zbMATH Keywords: Souslin number
zbMATH Keywords: density
zbMATH Keywords: weight
zbMATH Keywords: tightness
zbMATH Keywords: \(\pi\)-character
zbMATH Keywords: precaliber
zbMATH Keywords: monolithic space
zbMATH Keywords: homogeneous space
author: A. V. Arhangel'skii
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2007.04.025
OpenAlex ID: W2077447091
cites work: Q5614441
cites work: Q5644755
cites work: Q3029769
cites work: Homogeneity in powers of zero-dimensional first-countable spaces
cites work: Q4150804
cites work: Q5185667
cites work: Q3938195
cites work: Q3226265
cites work: Q3876676
cites work: Q3950745
cites work: Q4089499
cites work: MAPS ONTO TIKHONOV CUBES
cites work: Q3948292
cites work: A new bound on the cardinality of homogeneous compacta
DOI: 10.1016/J.TOPOL.2007.04.025
description: scientific article; zbMATH DE number 5365227