Tightness in product spaces
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- by U. N. B. Dissanayake and S. W. Willard PDF
- Proc. Amer. Math. Soc. 96 (1986), 136-140 Request permission
Abstract:
A product $\prod {X_i}$ of topological spaces ${X_i},i \in I$ will be said to preserve tightness if \[ \partial \left ( {\prod {X_i}} \right ) \leq \left | I \right | \cdot {\text {sup}}\left \{ {\partial \left ( {{X_i}} \right )\left | {i \in I} \right .} \right \}\] 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].References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 136-140
- MSC: Primary 54A25; Secondary 54B10, 54D30
- DOI: https://doi.org/10.1090/S0002-9939-1986-0813826-X
- MathSciNet review: 813826