TY - JOUR

T1 - Quotient spaces determined by algebras of continuous functions

AU - Lazar, Aldo J.

PY - 2010

Y1 - 2010

N2 - We prove that if X is a locally compact σ-compact space, then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if X is second countable locally compact, then γ(X) is second countable locally compact Hausdorff if and only if it is first countable. The interest in these results originated in [1] and [7] where the primitive ideal space of a C*-algebra was considered.

AB - We prove that if X is a locally compact σ-compact space, then on its quotient, γ(X) say, determined by the algebra of all real valued bounded continuous functions on X, the quotient topology and the completely regular topology defined by this algebra are equal. It follows from this that if X is second countable locally compact, then γ(X) is second countable locally compact Hausdorff if and only if it is first countable. The interest in these results originated in [1] and [7] where the primitive ideal space of a C*-algebra was considered.

UR - http://www.scopus.com/inward/record.url?scp=80054858238&partnerID=8YFLogxK

U2 - 10.1007/s11856-010-0075-0

DO - 10.1007/s11856-010-0075-0

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AN - SCOPUS:80054858238

SN - 0021-2172

VL - 179

SP - 145

EP - 155

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -