Topological coarse shape groups of compact metric spaces
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DOI: 10.21857/9xn31cvr1y
Abstract: The shape theory and, relatively new, coarse shape theory are very useful in studying of topological spaces, as well as of the corresponding algebraic invariants, especially, shape and coarse shape groups. By using certain ultrametrics… read more here.
Keywords: shape; topological coarse; shape groups; metric spaces ... See more keywords
A Note on Finite Coarse Shape Groups
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DOI: 10.3390/axioms12040377
Abstract: In this paper, we investigate properties concerning some recently introduced finite coarse shape invariants—the k-th finite coarse shape group of a pointed topological space and the k-th relative finite coarse shape group of a pointed… read more here.
Keywords: coarse shape; shape groups; finite coarse; shape group ... See more keywords
The Finite Coarse Shape Paths
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DOI: 10.3390/math13030439
Abstract: In this paper, we introduce the notions of finite coarse shape path and finite coarse shape path connectedness of a topological space. We prove that the solenoid Σ(pn), which is known to be coarse shape… read more here.
Keywords: shape path; coarse shape; path connected; finite coarse ... See more keywords