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Mathematical Notes

, Volume 62, Issue 6, pp 675–682 | Cite as

Obstructions to the extension of partial maps

  • S. M. Ageev
  • S. A. Bogatyi
Article
  • 33 Downloads

Abstract

One of the most important problems in topology is the minimization (in some sense) of obstructions to extending a partial map\(Z \leftarrow A\xrightarrow{f}X\), i.e., of a subsetF ⊂ Z/A such thatf can be globally extended to its complement. It is shown that ifZ is a fixed metric space with dimZ ≤ n andp, q ≥−1 are fixed numbers, then obstructions to extending all partial maps\(Z \leftarrow A\xrightarrow{f}X \in LC^p \cap C^4 \) can be concentrated in preselected fairly thin subsets ofZ.

Key words

partial map obstruction to extension Morita filtration selection set-valued lower semicontinuous map Lefschetz conditions connected locally connected spaces covers homotopy polyhedron 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. M. Ageev
    • 1
  • S. A. Bogatyi
    • 2
  1. 1.A. S. Pushkin Brest State Pedagogical InstituteBushkinUSSR
  2. 2.M. V. Lomonosov Moscow State UniversityMoscowUSSR

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