Kąkol, Jerzy and López Pellicer, Manuel and Martín Peinador, Elena and Tarieladze, Vaja (2008) Lindelöf spaces C(X) over topological groups. Forum Mathematicum, 20 (2). pp. 201212. ISSN 09337741

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Abstract
Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and sigmacompact. (ii) Cp(X) is analytic. (iii) Cp(X) is Kanalytic. (iv) Cp(X) is Lindelof. (v) Cc(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 Cp(X) is Lindelof iff Cc(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.
Item Type:  Article 

Uncontrolled Keywords:  Locally convexspaces; Banachspaces; Compactgroups; Property; Sets 
Subjects:  Sciences > Mathematics > Topology 
ID Code:  12712 
Deposited On:  13 May 2011 11:14 
Last Modified:  06 Feb 2014 09:30 
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