Open and other kinds of extensions over local compactifications
Abstract
Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set ((X),) of all (up to equivalence) locally compact Hausdorff extensions of a Tychonoff space X. Using this description, we find the necessary and sufficient conditions which has to satisfy a map between two Tychonoff spaces in order to have some kind of extension over arbitrary given in advance Hausdorff local compactifications of these spaces; we regard the following kinds of extensions: open, quasi-open, skeletal, perfect, injective, surjective. In this way we generalize some results of V. Z. Poljakov.
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