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

Alexander V. Arhangelskii

Vol. 18 (1966), No. 2, 201–208

DOI: 10.2140/pjm.1966.18.201

Abstract

The purpose of this paper is to show, under very general circumstances, that if f : X → Y is a closed map, then f⁻¹y 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