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Answering a question of Isbell we show that there exists a rim-compact space X such that every compactification Y of X has dim(Y)≥ 1.
CONTENTS I Introduction 1.1. Introductory remarks.................................................. 5 1.2. Baire spaces............................................................... 6 1.3. Completeness properties......................................... 8 1.4. Conventions................................................................. 9 II. Global completeness 2.1. The global completeness properties..................... 11 2.2. Products and subspaces.............................................
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