Properties of weak -refinable spaces

Author:
J. C. Smith

Journal:
Proc. Amer. Math. Soc. **53** (1975), 511-517

MSC:
Primary 54D20

MathSciNet review:
0380731

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Abstract: A space is called *weak* -*refinable* if every open cover of has a refinement satisfying (1) is an open collection for each , (2) each has finite positive order with respect to some , (3) the open cover is point finite.

In this paper the author shows that the above property lies between the properties of -refinable and weak -refinable. The main result is the fact that if is countably metacompact and satisfies property , every weak -cover of has a countable subcover. Results concerning paracompactness, metacompactness and the star-finite property are also obtained.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1975-0380731-8

Keywords:
-refinable,
weak -refinable,
countably compact,
compact,
paracompact,
metacompact,
property ,
discretely expandable,
Lindelöf,
starfinite property,
quasi-developable

Article copyright:
© Copyright 1975
American Mathematical Society