Original scientific paper

https://doi.org/10.3336/gm.45.2.17

On inverse limits of compact spaces. Correction of a proof

Sibe Mardešić ; Department of Mathematics, University of Zagreb, P.O.Box 335, 10 002 Zagreb, Croatia

Abstract

For a compact Hausdorff space X and an ANR for metrizable spaces M, one considers the space MX of all mappings from X to M, endowed with the compact-open topology. Since a mapping f: X' → X induces a natural mapping Mf : MX → MX', an inverse system of compact Hausdorff spaces X determines a direct system M X of spaces as well as the corresponding direct system of singular homology groups Hn(M X;G). There is a natural isomorphism between the direct limit dir lim Hn(M X;G) and the singular homology group Hn(MX;G), where X= inv lim X. This continuity theorem, used by some authors, was published more than 50 years ago. Unfortunately, the author discovered a serious error in the proofs of two lemmas on which the result depended. The present paper gives new correct proofs of these lemmas.

Keywords

Homology of spaces of mappings; compact Hausdorff space; absolute neighborhood retract; absolute neighborhood extensor; direct system; inverse system

Hrčak ID:

62705

URI

https://hrcak.srce.hr/62705

Publication date:

24.12.2010.

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