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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Lattices of topological extensions


Authors: John Mack, Marlon Rayburn and Grant Woods
Journal: Trans. Amer. Math. Soc. 189 (1974), 163-174
MSC: Primary 54D40
MathSciNet review: 0350700
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Abstract: For completely regular Hausdorff spaces, we consider topological properties P which are akin to compactness in the sense of Herrlich and van der Slot and satisfy the equivalent of Mrowka's condition (W). The algebraic structure of the family of tight extensions of X (which have P and contain no proper extension with that property) is studied. Where X has P locally but not globally, the relations between the complete lattice $ {P^ \ast }(X)$ of those tight extensions which are above the maximal one-point extension and the topology of the P-reflection are investigated and conditions found under which $ {P^\ast}(X)$ characterizes $ \gamma X - X$. The results include those of Magill on the lattice of compactifications of a locally compact space, and other applications are considered.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0350700-6
PII: S 0002-9947(1974)0350700-6
Keywords: P-reflection, lattice of tight P-extensions, compact, realcompact, almost realcompact, m-bounded
Article copyright: © Copyright 1974 American Mathematical Society