Monotone open images of 0-spaces (Q1316311)

A Tykhonov space \(X\) is called a 0-space whenever it has a compactification with a zero-dimensional remainder, whereas it is called rimcompact if it has a base which consists of open sets with compact boundaries. Each rimcompact space is a 0-space but the converse does not hold. A continuous map is called monotone provided that preimages of points are connected. The main result of this paper says that the property of being a 0-space is preserved under monotone open mappings. In the rimcompact case the result was obtained by \textit{T. A. Kuznetsova} [Mosc. Univ. Math. Bull. 28(1973), No. 5/6, 40-44 (1974); translation from Vestn. Mosk. Univ., Ser. I Mat. Mekh. 28, No. 5, 48-53 (1973; Zbl 0268.54022)]. A similar result for almost rimcompact spaces is presented as well.