Homotopy Theory of Micro Topological Spaces
DOI:
https://doi.org/10.24237/Keywords:
micro space, micro continuous, micro Homotopy, micro homotopy equivalentAbstract
This article looks at the link between homotopy theory and micro topological spaces, focusing on the new ideas that have come up: micro homotopy and micro homotopy equivalence. By extending classical homotopy to micro topological spaces, we capture more complex structural features at an infinitesimal scale. Micro homotopy is a continuous change between maps that keeps the microstructure of the spaces that are involved. Two micro topological spaces are micro homotopy equivalent if there exist micro continuous maps between them whose compositions are micro homotopic to the respective identity maps. These ideas give us a better way to think about equivalence in topological analysis.
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