J Austral Math Soc Ser A 44 pp252--258, 1988.

LECs, Local Mixers, Topological Groups and Special Products

Carlos E. Borges

Abstract

We prove that every (locally) contractible topological group is (L)EC and apply these results to homeomorphism groups, free topological groups, reduced products and symmetric products. Our main results are: The free topological group of a q-contractible space is equiconnected. A paracompact and weakly locally contractible space is locally equiconnected if and only if it has a local mixer. There exist compact metric contractible spaces X whose reduced (symmetric) products are not retracts of the Graev free topological groups F(X) (A(X)) (thus correcting results we published ibidem).

1980 AMS Subject Classification: primary 54C55; secondary 22A05, 57S05

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Authors

Carlos R. Borges

Department of Mathematics, University of California, Davis, California 95616, U.S.A.