Vol. 18, No. 2, 1966

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On closed mappings, bicompact spaces, and a problem of P. Aleksandrov

Alexander V. Arhangelskii

Vol. 18 (1966), No. 2, 201–208
Abstract

The purpose of this paper is to show, under very general circumstances, that if f : X Y is a closed map, then f1y must be bicompact for “most” y Y . Two theorems of this sort are obtained, one of which is then used to answer a question of P. Alexandroff on the effect of closed maps on countable-dimensional spaces.

Mathematical Subject Classification
Primary: 54.60
Milestones
Received: 14 May 1965
Published: 1 August 1966
Authors
Alexander V. Arhangelskii