Fiber Strong Shape Theory for Topological Spaces

Vladimer Baladze; Ruslan Tsinaridze

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arXiv · 1703.10374

Fiber Strong Shape Theory for Topological Spaces

Vladimer Baladze·Ruslan Tsinaridze

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Abstract

In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space $\Bo$. Our approach is based on the method of Mardešić-Lisica and instead of resolutions, introduced by Mardešić, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over $\Bo$ which is coarser than the classification of spaces over $\Bo$ induced by fiber homotopy theory, but is finer than the classification of spaces over $\Bo$ given by usual fiber shape theory.

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BibTeX RIS

Vladimer Baladze, Ruslan Tsinaridze. 2017-03-30. Fiber Strong Shape Theory for Topological Spaces. https://arxiv.org/abs/1703.10374

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