The space of all p-th roots of a nilpotent complex matrix is path-connected
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DOI: 10.1016/j.laa.2020.02.028
Abstract: Let p be a positive integer and A be a nilpotent complex matrix. We prove that the set of all p-th roots of A is path-connected. read more here.
Keywords: complex matrix; nilpotent complex; space roots; path connected ... See more keywords
The set of uniquely ergodic interval exchange transformations is path-connected
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DOI: 10.1017/etds.2017.34
Abstract: Let $\unicode[STIX]{x1D70B}$ be a non-degenerate permutation on at least four symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\unicode[STIX]{x1D70B}$ is path-connected. read more here.
Keywords: uniquely ergodic; interval exchange; ergodic interval; set uniquely ... 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