Cellularity of a space of subgroups of a discrete group

A. Leiderman; I. V. Protasov

Cellularity of a space of subgroups of a discrete group

A. Leiderman, I. V. Protasov

Department of Mathematics

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

1 Scopus citations

Abstract

Given a discrete group G, we consider the set L(G) of all subgroups of G endowed with topology of pointwise convergence arising from the standard embedding of L(G) into the Cantor cube (0, 1)^G. We show that the cellularity c(L(G)) ≤ ℵ₀ for every abelian group G, and, for every infinite cardinal τ we construct a group G with c(L(G)) =τ.

Original language	English
Pages (from-to)	519-522
Number of pages	4
Journal	Commentationes Mathematicae Universitatis Carolinae
Volume	49
Issue number	3
State	Published - 1 Jan 2008

Keywords

Cellularity
Shanin number
Space of subgroups

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "Given a discrete group G, we consider the set L(G) of all subgroups of G endowed with topology of pointwise convergence arising from the standard embedding of L(G) into the Cantor cube (0, 1)G. We show that the cellularity c(L(G)) ≤ ℵ0 for every abelian group G, and, for every infinite cardinal τ we construct a group G with c(L(G)) =τ.",

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AU - Protasov, I. V.

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N2 - Given a discrete group G, we consider the set L(G) of all subgroups of G endowed with topology of pointwise convergence arising from the standard embedding of L(G) into the Cantor cube (0, 1)G. We show that the cellularity c(L(G)) ≤ ℵ0 for every abelian group G, and, for every infinite cardinal τ we construct a group G with c(L(G)) =τ.

AB - Given a discrete group G, we consider the set L(G) of all subgroups of G endowed with topology of pointwise convergence arising from the standard embedding of L(G) into the Cantor cube (0, 1)G. We show that the cellularity c(L(G)) ≤ ℵ0 for every abelian group G, and, for every infinite cardinal τ we construct a group G with c(L(G)) =τ.

KW - Cellularity

KW - Shanin number

KW - Space of subgroups

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Cellularity of a space of subgroups of a discrete group

Abstract

Keywords

ASJC Scopus subject areas

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