Atlas: Continua whose homeomorphism groups are generated by small neighborhoods of the identity by Wayne Lewis

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First International Meeting on Continuum Theory
June 29 - July 1, 2000
Facultad de Ciencias Fisico-Matematicas de la Benemerita Universidad Autonoma de Puebla
Puebla, Mexico

Organizers
Raul Escobedo, Fernando Macias, Sergio Macias, Richard Schori, Carl Seaquist

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Continua whose homeomorphism groups are generated by small neighborhoods of the identity
by
Wayne Lewis
Texas Tech University
Coauthors: Zhou Youcheng (Zhejiang University)

The first author has shown that the pseudo-arc P has the property that, for every \epsilon > 0, every homeomorphism of P is a composition of a finite number of homeomorphisms each of which moves no point a distance greater than \epsilon. A compactum with the property that its homeomorphism group is generated by arbitrarily small neighborhoods of the identity is said to have a micro-generated homeomorphism group. A homeomorphism of a compactum which is a composition of homeomorphisms in an arbitrarily small neighborhood of the identity is said to be micro-generated. We discuss results on homeomorphisms of continua which are micro-generated and on continua which have micro-generated homeomorphism groups.

Date received: April 10, 2000