Point Degree Spectra of Represented Spaces
Forum of Mathematics, Sigma, Tome 10 (2022)
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We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees and so on. The notion of point degree spectrum creates a connection among various areas of mathematics, including computability theory, descriptive set theory, infinite-dimensional topology and Banach space theory. Through this new connection, for instance, we construct a family of continuum many infinite-dimensional Cantor manifolds with property C whose Borel structures at an arbitrary finite rank are mutually nonisomorphic. This resolves a long-standing question by Jayne and strengthens various theorems in infinite-dimensional topology such as Pol’s solution to Alexandrov’s old problem.
@article{10_1017_fms_2022_7,
author = {Takayuki Kihara and Arno Pauly},
title = {Point {Degree} {Spectra} of {Represented} {Spaces}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.7/}
}
Takayuki Kihara; Arno Pauly. Point Degree Spectra of Represented Spaces. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.7
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