Extremally disconnected remainders of nowhere locally compact spaces

The main result of this paper is Theorem 2.2. It says that if X is a Tychonoff nowhere locally compact nonpseudocompact space with an extremally disconnected remainder Z (in some Hausdorff compactification bX of X), then X contains a nonempty open in X extremally disconnected subspace. A variety of corollaries, versions, and generalizations of this result is also presented. An important feature of almost all results below is that the spaces under consideration are assumed to be nowhere locally compact. (c) 2022 Elsevier B.V. All rights reserved.