HFD and HFC type spaces, with applications
type: Item
instance of: scholarly article
title: HFD and HFC type spaces, with applications
zbMATH Open document ID: 1012.54003
DOI: 10.1016/S0166-8641(02)00080-9
author: István Juhász
published in: Topology and its Applications
publication date: 2003-04-02T00:00:00Z
review text: HFD's and HFC's arose early in the study of S and L spaces, gave rise to variations (e.g., HFD\(_{\text{w}}\)'s and HFC\(_{\text{w}}\)'s) and have been intensely studied by Juhász and his colleagues in Budapest. They are subspaces of Cantor cubes \(2^{\kappa}\) with strong combinatorial properties designed to give rise to interesting topological properties. This survey paper discusses their properties, relates them to other combinatorial principles, and studies the consequences of their properties for topology and vice versa (for example, the existence of 0-dimensional Hausdorff spaces in which every large subspace is separable but there is a small non-separable subspace; or spaces with properties similar to Ostaszewski spaces). To give the reader a taste of what this is about: a space \(X \subset 2^{\kappa 1}\) is HFD iff for every countable \(A \subset X\) there is a countable \(B \subset \kappa\) such that \(A|_{\kappa \setminus B}\) is dense in \(2^{\kappa \setminus B}\). Basic results are: HFD's are hereditarily separable, have no non-trivial convergent sequences, and are hereditarily collectionwise normal.
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 1891209
zbMATH Keywords: HFD and HFC spaces
zbMATH Keywords: S and L spaces
zbMATH Keywords: cardinal functions
zbMATH Keywords: independence results
zbMATH Keywords: Cantor cubes
reviewed by: Judith Roitman
MaRDI profile type: Publication
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full work available at URL: s0166-8641(02)00080-9
OpenAlex ID: W1999231769
description: scientific article; zbMATH DE number 1891209