Compact dispersed spaces and the -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

DOI:
https://doi.org/10.1090/S0002-9939-1983-0687653-8

MathSciNet review:
687653

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

**[A]**A. V. Arhangel'skij,*On topologies admitting a weak connection with orders*, Soviet Math. Dokl.**19**(1978), 77-81.**[A]**-,*On**-expanded spaces*, Soviet Math. Dokl.**19**(1978), 336-340.**[GJu]**J. Gerlits and I. Juhász,*On left-separated compact spaces*, Comment. Math. Univ. Carolinae**19**(1978), 53-62. MR**0487982 (58:7561)****[J]**T. Jech,*Set theory*, Academic Press, New York, 1978. MR**506523 (80a:03062)****[P]**S. Purisch,*Scattered compactifications and the orderability of scattered spaces*, Topology Appl.**12**(1981), 83-88. MR**600466 (82m:54030)****[R]**W. Rudin,*Continuous functions on compact spaces without perfect subsets*, Proc. Amer. Math. Soc.**8**(1957), 39-42. MR**0085475 (19:46b)****[S]**A. H. Stone,*Kernel constructions and Borel sets*, Trans. Amer. Math. Soc.**107**(1963), 58-70. MR**0151935 (27:1916)****[T]**R. Telgársky,*Total paracompactness and paracompact dispersed spaces*, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.**16**(1978), 567-572. MR**0235517 (38:3826)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0687653-8

Keywords:
Left separated space,
-left space,
left well order,
orderable space (LOTS),
dispersed space,
ordinal space

Article copyright:
© Copyright 1983
American Mathematical Society