Abstract
All spaces considered are completely regular and X* denotes βX — X. The point x G X* is called a remote point of X if x g C\βxA for each nowhere dense subset A of X. If y G 7, then the space Y is said to be extremally disconnected at y if j> £ ί/ Π F whenever £/and Fare disjoint open sets. In this paper we construct two noncompact σ-compact spaces X, one locally compact and one nowhere locally compact, such that X has no remote points, and in fact such that βX is not extremally disconnected at any point.
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