TY - JOUR

T1 - On Degree Spectra of Topological Spaces

AU - Selivanov, V. L.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - Abstract: The investigation of computability in topological structures develops in some aspects similar to the investigation of computability in algebraic structures. If a countable algebraic structure is not computably presentable then its ‘‘degree of non-computability’’ is measured by the so called degree spectrum, i.e. the set of Turing degrees that compute an isomorphic copy of the structure. In this note we initiate a discussion of similar notions for topological structures, in particular we describe the degree spectra of domains.

AB - Abstract: The investigation of computability in topological structures develops in some aspects similar to the investigation of computability in algebraic structures. If a countable algebraic structure is not computably presentable then its ‘‘degree of non-computability’’ is measured by the so called degree spectrum, i.e. the set of Turing degrees that compute an isomorphic copy of the structure. In this note we initiate a discussion of similar notions for topological structures, in particular we describe the degree spectra of domains.

KW - Algebraic structure

KW - degree spectrum

KW - topological structure

KW - Turing degree

UR - http://www.scopus.com/inward/record.url?scp=85087890495&partnerID=8YFLogxK

U2 - 10.1134/S1995080220020146

DO - 10.1134/S1995080220020146

M3 - Article

AN - SCOPUS:85087890495

VL - 41

SP - 252

EP - 259

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 2

ER -