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  • LECs, Local Mixers, Topological Groups and Special Products

  • Part of
  • Carlos R. Borges
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 44 / Issue 2 / April 1988
    Published online by Cambridge University Press:
    09 April 2009, pp. 252-258
    Print publication:
    April 1988
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  • 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 θ-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).