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Products and Cardinal Invariants of Minimal Topological Groups

Published online by Cambridge University Press:  20 November 2018

Douglass L. Grant  and
W. W. Comfort
Douglass L. Grant
Affiliation:
University College of Cape Breton, Box 5300, Sydney, Nova Scotia, Canada BIP 6L2
W. W. Comfort
Affiliation:
University College of Cape Breton, Box 5300, Sydney, Nova Scotia, Canada BIP 6L2
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Abstract

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It is a question of Arhangel'skiĭ [1] (Problem 2) whether the identity ψ(G) = X(G) holds for every minimal Hausdorff topological group G = 〈G,u〉). (Here, as usual, ψ(G), the pseudocharacter of G, is the least cardinal number K for which there is such that and and x(G), the character of G,is the least cardinality of a local base at e for (〈G,u〉.) That 〈G, u〉 is minimal means that, if v is a Hausdorff topological group topology for G and v ⊂ u, then v = u.

In this paper, we give some conditions on G sufficient to ensure a positive response to Arhangel'skiï's question, and we offer an example which responds negatively to a question on minimal groups posed some years ago (cf. [6] (p. 107) and [4] (p. 259)).

Keywords

Primary 54A2554D25Secondary 22A0554A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 44 - 49
Copyright
Copyright © Canadian Mathematical Society 1986

References

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