Open and other kinds of extensions over local compactifications

Details Open and other kinds of extensions over local compactifications Open and other kinds of extensions over local compactifications

2009-10-17

arxiv.org/abs/0910.3254v1

Mathematics

General Topology

22 pages

Scientific paper

Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set $(\LL(X),\le)$ 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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