RT Journal Article
T1 Lindelöf spaces C(X) over topological groups
A1 Kąkol, Jerzy
A1 López Pellicer, Manuel
A1 Martín Peinador, Elena
A1 Tarieladze, Vaja
AB Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and sigma-compact. (ii) C-p(X) is analytic. (iii) C-p(X) is K-analytic. (iv) C-p(X) is Lindelof. (v) C-c(X) is a separable metrizable and complete locally convex space. (vi) C,(X) is compactly dominated by irrationals. This result supplements earlier results of Corson, Christensen and Calbrix and provides several applications, for example, it easily applies to show that: (1) For a compact topological group X the Eberlein, Talagrand, Gul'ko and Corson compactness are equivalent and any compact group of this type is metrizable. (2) For a locally compact topological group X the space C-p(X) is Lindelof iff C-c(X) is weakly Lindelof. The proofs heavily depend on the following result of independent interest: A locally compact topological group X is metrizable iff every compact subgroup of X has countable tightness (Theorem 2). More applications of Theorem 1 and Theorem 2 are provided.
PB WALTER DE GRUYTER
SN 0933-7741
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/49681
UL https://hdl.handle.net/20.500.14352/49681
LA eng
NO Komitet Badan´ Naukowych (State Committee for Scientific Research)
NO Ministery of Education and Science
NO MTM
NO BFM
NO FEDER
DS Docta Complutense
RD 22 abr 2025