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Obstructions to the extension of partial maps. (English. Russian original) Zbl 0936.54025

Math. Notes 62, No. 6, 675-682 (1997); translation from Mat. Zametki 62, No. 6, 803-812 (1997).
Summary: One of the most important problems in topology is the minimization (in this or another sense) of obstructions to the extension of the partial map \(Z\hookleftarrow A@>f>>X\), i.e. of a subset \(F\subset Z \smallsetminus A\) such that \(f\) can globally be extended to its complement. It is shown that if a metric space \(Z\), \(\dim Z\leq n\), and numbers \(p,q\geq -1\) are fixed, then the obstructions to all partial maps \(Z\hookleftarrow A@>f>> X\in LC^p \cap C^q\) can be concentrated in preselected fairly thin subsets of \(Z\).

MSC:

54C20 Extension of maps
55S35 Obstruction theory in algebraic topology
54C65 Selections in general topology
54C15 Retraction
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References:

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