Homeomorphism groups of dendrons

Beverly L. Brechner

Vol. 28 (1969), No. 2, 295–301

DOI: 10.2140/pjm.1969.28.295

Abstract

Professor J. Dugundji has asked the following question. Is the space of homeomorphisms of a contractible, locally contractible, space necessarily locally contractible? In this paper we answer the question in the negative by showing that the spaces of homeomorphisms of certain dendrons are not locally contractible. Specifically, we will show that any “special” dendron (see Definition 2.3) has a zero dimensional, non-discrete, group of homeomorphisms.

Mathematical Subject Classification

Primary: 54.80

Milestones

Received: 30 January 1968

Revised: 3 June 1968

Published: 1 February 1969