Fine shape III: $\Delta$-spaces and $\nabla$-spaces

Sergey A. Melikhov

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arXiv · 2211.11101

Fine shape III: $\Delta$-spaces and $\nabla$-spaces

Sergey A. Melikhov

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Abstract

In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dimensional metrizable spaces and their homology theories. We show that every Polish space $X$ is fine shape equivalent to the limit of an inverse sequence of simplicial maps between metric simplicial complexes. A deeper result is that if $X$ is locally finite dimensional, then the simplicial maps can be chosen to be non-degenerate. They cannot be chosen to be non-degenerate if $X$ is the Taylor compactum.

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BibTeX RIS

Sergey A. Melikhov. 2022-11-20. Fine shape III: $\Delta$-spaces and $\nabla$-spaces. https://arxiv.org/abs/2211.11101

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