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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tightness in product spaces


Authors: U. N. B. Dissanayake and S. W. Willard
Journal: Proc. Amer. Math. Soc. 96 (1986), 136-140
MSC: Primary 54A25; Secondary 54B10, 54D30
MathSciNet review: 813826
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Abstract: A product $ \prod {X_i}$ of topological spaces $ {X_i},i \in I$ will be said to preserve tightness if

$\displaystyle \partial \left( {\prod {X_i}} \right) \leq \left\vert I \right\ve... ...}\left\{ {\partial \left( {{X_i}} \right)\left\vert {i \in I} \right.} \right\}$

where $ \partial \left( X \right)$ denotes the tightness of $ X$.

We show $ \prod {X_i}$ preserves tightness whenever each finite subproduct does. It is further shown that this is the case whenever each $ {X_i}$ is a locally compact $ {T_2}$-space, and whenever each $ {X_i}$ is a locally Lindelöf $ {T_3}$ $ P$-space, extending 5.9 in [J].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813826-X
PII: S 0002-9939(1986)0813826-X
Keywords: Tightness, product space, $ m - n$ compact space, $ < n$-discrete space
Article copyright: © Copyright 1986 American Mathematical Society