The product of two ordinals is hereditarily dually discrete.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1249.54051
author: M. Á. Gaspar-Arreola
author: Fernando Hernández-Hernández
publication date: 2012-07-10T00:00:00Z
full work available at URL: https://eudml.org/doc/246121
full work available at URL: cmuc1201.htm
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 03E10
zbMATH DE Number: 6054290
zbMATH Keywords: dually discrete space
zbMATH Keywords: stationary set
zbMATH Keywords: ordinal space
MaRDI profile type: Publication
title: The product of two ordinals is hereditarily dually discrete.
published in: Commentationes Mathematicae Universitatis Carolinae
review text: The main result is the following theorem: Let \(\mu \) and \(\nu \) be two ordinals (considered with the order topology) and let \(Y\) be an arbitrary subset of the product \(\mu \times \nu \). Then \(Y\) is dually discrete, that is, for any neighborhood assignment \(y\mapsto \phi (y)\), \(y\in Y\), there is a discrete subset \(D\subset Y\) (not necessarily closed) such that the sets \(\phi (y)\), \(y\in D\), cover \(Y\).NEWLINENEWLINEThis result was independently proved by \textit{L.-X. Peng} [Topology Appl. 159, No. 1, 304--307 (2012; Zbl 1234.54034)] using a very similar method.
reviewed by: Ondřej F. K. Kalenda
description: scientific article; zbMATH DE number 6054290