Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular). The book offers detailed, self-contained proofs of many of the key results.

1. Introduction. 1.1. Background. 1.2. Baire and Related Spaces. 1.3. Quasicontinuous Functions. 1.4. Set-Valued Mappings. 1.5. Basics of Function Spaces. 1.6. Concepts in Banach Spaces. 1.7. Commentary and Exercises. 2. Fundamental Results. 2.1. Fundamental Questions. 2.2. First Countable Spaces. 2.3. q-Spaces. 2.4. Second Countable Spaces. 2.5. Separately Quasicontinuous Functions. 6. Piotrowski’s Theorem. 2.7. Talagrand’s Problem. 2.8. Commentary and Exercises. 3. Continuity of Group Actions and Operations. 3.1. Semitopological and Paratopological Groups. 3.2. Δ-Baire Spaces. 3.3. Continuity of Group Actions. 3.4. Some Counterexamples. 3.5. Miscellaneous Applications. 3.6. Commentary and Exercises. 4. Namioka Theorem and Related Spaces. 4.1. Namioka Theorem. 4.2. Namioka Theorem - a Functional Analytic Proof. 4.3. Namioka Spaces. 4.4. Co-Namioka Spaces. 4.5. Commentary and Exercises. 5. Various Applications. 5.1. Point of Continuity Properties. 5.2. Minimal USCO Mappings. 5.3. Ryll-Nardzewski Fixed-Point Theorem. 5.4. Differentiability of Continuous Convex Functions. 5.5. Applications in Variational Analysis. 6. Future Directions and Open Problems. 6.1. Topologies of Separate and Joint Continuity. 6.2. Semitopological and Paratopological Groups. 6.3. Namioka Spaces. 6.4. Co-Namioka and Related Spaces. 6.5. Baire Measurability of Separately Continuous Functions. 6.6. Sets of Discontinuity Points of Separately Continuous Functions. 6.7. Various Maslyuchenko Spaces.