Characterizations of arboroids and dendritic spaces

Thomas Bourque Muenzenberger, Raymond Earl Smithson and L. E. Ward

Vol. 102 (1982), No. 1, 107–121

DOI: 10.2140/pjm.1982.102.107

Abstract

In this paper several characterizations of arboroids, arcwise connected dendritic spaces, and a related, wider class of spaces which we call weakly nested are obtained. For example, it is shown that an arcwise connected Hausdorff space is dendritic if and only if it is uniquely arcwise connected and each connected subspace is arcwise connected. These characterizations give considerable insight into the internal structure of such spaces. Also a number of characterizations of topological intervals and trees are given, and an interesting embedding theorem for weakly nested spaces is proved.

Mathematical Subject Classification 2000

Primary: 54F65

Secondary: 54F50, 54F20

Milestones

Received: 21 April 1981

Published: 1 September 1982