STRUCTURE AND CLASSIFICATION OF TOPOLOGICAL SPACES AND CARDINAL INVARIANTS

Abstract

CONTENTS Introduction Some special terminology and notation Chapter I. Cardinal invariants in broad classes of spaces § 1. Basic cardinal invariants. Typical relations and problems § 2. Cardinal invariants and extendability properties § 3. Particular features of the cardinal structure of ordered spaces and their images § 4. Bounds using the Suslin number and invariants of the type of the character § 5. On the behaviour of certain cardinal invariants under multiplication § 6. The spread, the hereditary Lindelöf number, and the hereditary density § 7. π-weight and topological homogeneity Chapter II. The structure of compact spaces and cardinal invariants § 1. The simplest non-trivial facts § 2. Tightness of compact spaces and free sequences § 3. Tightness and products. Connection with compactifications Chapter III. The maps and the structure of compact spaces § 1. Images of products and Σ-products. Reciprocal questions § 2. Irreducible maps into Σ-products of intervals. Some consequences of Martin's axiom § 3. Non-homogeneity of infinite extremally disconnected compact spaces Chapter IV. Topological properties of mapping spaces § 1. Typical problems and results § 2. Functional closure and functional tightness § 3. Shchepin's spectral theorem and the tightness of mapping spaces § 4. Some other results about function spaces Open problems References