On the sobrification remainder ^sX −X

Rudolf-Eberhard Hoffmann

Vol. 83 (1979), No. 1, 145–156

DOI: 10.2140/pjm.1979.83.145

Abstract

The topics of this paper are (1) a study of the sobrification remainder ^sX −X (hence our title), (2) a new, simple proof of the characterization of T_D-spaces Y as those spaces Y such that Y is the smallest subspace X of ^sY for which the embedding X↪^sY is the universal sobrification, (3) an elegant characterization of Noetherian sober spaces. These themes are linked by the common tool by aid of which they are investigated, the so-called b-topology L. Skula [28].

Mathematical Subject Classification 2000

Primary: 54D40

Milestones

Received: 13 March 1978

Revised: 29 November 1978

Published: 1 July 1979