Products of general Menger spaces

Piotr Szewczak; Boaz Tsaban

doi:https://doi.org/10.1016/j.topol.2019.01.005

Products of general Menger spaces

Piotr Szewczak, Boaz Tsaban

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the classic real line topology to the Michael topology. Among other results, we prove that, assuming the Continuum Hypothesis, every productively Lindelöf space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.

Original language	English
Pages (from-to)	41-55
Number of pages	15
Journal	Topology and its Applications
Volume	255
DOIs	https://doi.org/10.1016/j.topol.2019.01.005
State	Published - 15 Mar 2019

Keywords

Concentrated sets
Hurewicz property
Menger property
Product spaces
Productively Hurewicz
Productively Lindelöf
Productively Menger

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1016/j.topol.2019.01.005

Cite this

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title = "Products of general Menger spaces",

abstract = "We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the classic real line topology to the Michael topology. Among other results, we prove that, assuming the Continuum Hypothesis, every productively Lindel{\"o}f space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.",

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T1 - Products of general Menger spaces

AU - Szewczak, Piotr

AU - Tsaban, Boaz

PY - 2019/3/15

Y1 - 2019/3/15

N2 - We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the classic real line topology to the Michael topology. Among other results, we prove that, assuming the Continuum Hypothesis, every productively Lindelöf space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.

AB - We study, in a systematic manner, products of general topological spaces with Menger's covering property, and its refinements based on filters and semifilters. To this end, we apply Dedekind compactification to extend the projection method from the classic real line topology to the Michael topology. Among other results, we prove that, assuming the Continuum Hypothesis, every productively Lindelöf space is productively Menger, and every productively Menger space is productively Hurewicz. None of these implications is reversible.

KW - Concentrated sets

KW - Hurewicz property

KW - Menger property

KW - Product spaces

KW - Productively Hurewicz

KW - Productively Lindelöf

KW - Productively Menger

UR - http://www.scopus.com/inward/record.url?scp=85060280910&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.topol.2019.01.005

DO - https://doi.org/10.1016/j.topol.2019.01.005

M3 - مقالة

SN - 0166-8641

VL - 255

SP - 41

EP - 55

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Products of general Menger spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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