On inverse limits of compact spaces. Correction of a proof (CROSBI ID 171090)
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Mardešić, Sibe
engleski
On inverse limits of compact spaces. Correction of a proof
For a compact Hausdorff space <i>X</i> and an ANR for metrizable spaces <i>M</i>, let <i>M<sup>X</sup></i> denote the space of all mappings from <i>X</i> to <i>M</i>, endowed with the compact-open topology. An inverse system <b><i>X</i></b> of compact Hausdorff spaces determines a direct system of spaces <i>M<sup><b>X</b></sup></i> and the corresponding direct system of singular homology groups <i>H<sub>n</sub></i>(<i>M<sup><b>X</b></sup></i> ; <i>G</i>). There is a natural isomorphism between the direct limit of the latter system and the singular homology group <i>H<sub>n</sub></i>(<i>M<sup>X</sup></i> ; <i>G</i> ) of the inverse limit <i>X</i> of <i><b>X</b></i>. This fact appears in a paper published by the author more than 50 years ago. However, the proofs of two of the lemmas used were erroneous. They are now replaced by correct proofs.
compact Hausdorff spaces; inverse limit; singular homology
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