Dendritic compactification

Keith Roy Allen

Vol. 57 (1975), No. 1, 1–10

DOI: 10.2140/pjm.1975.57.1

Abstract

Let X be a rim compact dendritic space. It is shown that the unique dendritic compactification of X is the same as the Freudenthal compactification of X. This compactification is characterized in terms of monotone maps from X into the closed unit interval, and is shown to be a GA compactification. An example is given to show that X need not have a convex cut point partial order, in order to have a dendritic compactification.

Mathematical Subject Classification 2000

Primary: 54D35

Secondary: 54F50

Milestones

Received: 30 August 1974

Published: 1 March 1975