Products and Cardinal Invariants of Minimal Topological Groups
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 44-49
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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)).
Grant, Douglass L.; Comfort, W. W. Products and Cardinal Invariants of Minimal Topological Groups. Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 44-49. doi: 10.4153/CMB-1986-008-x
@article{10_4153_CMB_1986_008_x,
author = {Grant, Douglass L. and Comfort, W. W.},
title = {Products and {Cardinal} {Invariants} of {Minimal} {Topological} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {44--49},
year = {1986},
volume = {29},
number = {1},
doi = {10.4153/CMB-1986-008-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-008-x/}
}
TY - JOUR AU - Grant, Douglass L. AU - Comfort, W. W. TI - Products and Cardinal Invariants of Minimal Topological Groups JO - Canadian mathematical bulletin PY - 1986 SP - 44 EP - 49 VL - 29 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-008-x/ DO - 10.4153/CMB-1986-008-x ID - 10_4153_CMB_1986_008_x ER -
%0 Journal Article %A Grant, Douglass L. %A Comfort, W. W. %T Products and Cardinal Invariants of Minimal Topological Groups %J Canadian mathematical bulletin %D 1986 %P 44-49 %V 29 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-008-x/ %R 10.4153/CMB-1986-008-x %F 10_4153_CMB_1986_008_x
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