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.......................................... 13 2.3. Mappings...................................................................... 15 2.4. Examples..................................................................... 17 III. Moore spaces 3.1. Moore completeness and Rudin completeness............................... 20 3.2. Countable global completeness in Moore spaces........................... 21 3.3. Moore spaces and Baire spaces......................................................... 24 IV. Local and almost completeness 4.1. Dense complete subspaces................................................................. 20 4.2. Products and subspaccs.................................................................................... 28 4.3. Mappings................................................................................................................ 30 V. Additional remarks 5.1. Miscellaneous topics.............................................................................. 34 5.2. Relations between the completeness properties............................. 37 5.3. Open problems........................................................................................ 40 References.................................................................................................................... 42
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