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LECs, Local Mixers, Topological Groups and Special Products

Part of: Topological and differentiable algebraic systems Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

Carlos R. Borges
Carlos R. Borges
Affiliation:
Department of MathematicsUniversity of CaliforniaDavis, California 95616, U.S.A.
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Abstract

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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).

Keywords

θ-contractiblefree topological groupreduced productsymmetric product(L)EC(local) mixershomeomorphism groups.

MSC classification

Secondary: 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 22A05: Structure of general topological groups 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 252 - 258
Copyright
Copyright © Australian Mathematical Society 1988

References

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