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Compact dispersed spaces and the $ \alpha $-left property

Authors: G. De Marco, A. Le Donne and R. G. Wilson
Journal: Proc. Amer. Math. Soc. 87 (1983), 737-742
MSC: Primary 54F99; Secondary 54F05
MathSciNet review: 687653
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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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Keywords: Left separated space, $ \alpha $-left space, left well order, orderable space (LOTS), dispersed space, ordinal space
Article copyright: © Copyright 1983 American Mathematical Society

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