On the closed images of paracomplexes

Takemi Mizokami

Vol. 97 (1981), No. 1, 183–195

DOI: 10.2140/pjm.1981.97.183

Abstract

Let X be an image of a paracomplex by a closed mapping. Then the following are proved: (1) X is an M₁-space, and this solves positively the problem proposed by J. Nagata, (2) dimX = Ind X, and (3) dimX ≦ n if and only if there exists a σ-closure-preserving base 𝒲 for X such that dimB(W) ≦ n − 1 for every W ∈𝒲.

Mathematical Subject Classification 2000

Primary: 54E20

Secondary: 54F45

Milestones

Received: 30 October 1980

Published: 1 November 1981