Compact dispersed spaces and the 𝛼-left property

De Marco, G.; Le Donne, A.; Wilson, R. G.

doi:10.1090/S0002-9939-1983-0687653-8

Compact dispersed spaces and the $\alpha$-left property
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by G. De Marco, A. Le Donne and R. G. Wilson PDF

Proc. Amer. Math. Soc. 87 (1983), 737-742 Request permission

Abstract:

The concept of an $\alpha$-left space was introduced by Arhangel’skij in [A$_{1}$], where, among other results, it was shown that every ${T_2}$ compact $\alpha$-left space is dispersed. In [A$_{2}$] an example was given to show that, assuming the continuum hypothesis CH, not every ${T_2}$ compact dispersed space is $\alpha$-left. The aim of this article is to obtain some sufficient conditions for ${T_2}$ space to be $\alpha$-left and to construct a large class (which contains all products of uncountable ordinals) of compact ${T_2}$ dispersed spaces which are not $\alpha$-left.

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