On dense subsets, convergent sequences and projections of Tychonoff products
type: Item
instance of: scholarly article
title: On dense subsets, convergent sequences and projections of Tychonoff products
zbMATH Open document ID: 1380.54013
published in: Topology and its Applications
publication date: 2017-11-22T00:00:00Z
review text: The author extends his work in [Topology Appl. 221, 300--308 (2017; Zbl 1379.54009)] to prove that in a product of continuum many non-trivial separable Hausdorff spaces one can find a countable dense set~\(Q\) such that whenever \(S\) is an infinite subset of~\(Q\) the projection of~\(S\) onto some countable subproduct is dense. In addition, the Tychonoff cube \([0,1]^\mathbb{R}\) is shown to have a countable dense subset as above that is closed and discrete in the box topology.
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 6811274
zbMATH Keywords: separable
zbMATH Keywords: independent matrix
zbMATH Keywords: discrete space
zbMATH Keywords: product
zbMATH Keywords: box product
zbMATH Keywords: convergent sequence
author: A. A. Gryzlov
reviewed by: K. P. Hart
MaRDI profile type: Publication
full work available at URL: j.topol.2017.10.021
OpenAlex ID: W2765549164
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DOI: 10.1016/J.TOPOL.2017.10.021
description: scientific article; zbMATH DE number 6811274