A+ CATEGORY SCIENTIFIC UNIT

The topological fixed point property — an elementary continuum-theoretic approach

Volume 77 / 2007

Roman Mańka Banach Center Publications 77 (2007), 183-200 MSC: Primary 54H25; Secondary 54F15. DOI: 10.4064/bc77-0-14

Abstract

A set contained in a topological space has the topological fixed point property if every continuous mapping of the set into itself leaves some point fixed. In 1969, R. H. Bing published his article The Elusive Fixed Point Property, posing twelve intriguing and difficult problems, which exerted a great influence on the study of the fixed point property. We now present a survey article intended for a broad audience that reports on this area of fixed point theory. The exposition is also intended to give an introduction to the current study of the fixed point property from the viewpoint of an elementary continuum theory.

Authors

  • Roman MańkaInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8,
    P.O.B. 21
    00-956 Warsaw, Poland
    e-mail

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