Separate and Joint Continuity

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.

Although the development of this area has now slowed to a point where an authoritative book can be written, many important and significant problems remain open, and it is hoped that this book may serve as a springboard for future and emerging researchers into this area. Furthermore, it is the strong belief of the authors that this area of research is ripe for exploitation. That is to say, it is their belief that many of the results contained in this monograph can, and should be, applied to other areas of mathematics. It is hoped that this monograph may provide an easily accessible entry point to the main results on separate and joint continuity for mathematicians who are not directly working in this field, but who may be able to exploit some of the deep results that have been developed over the past 125 years.

Features

• Provides detailed, self-contained proofs of many of the key results in the area
• Suitable for researchers and postgraduates in topology and functional analysis
• Is the first book to offer a detailed and up-to-date summary of the main ideas and theorems on this topic

Jiling Cao is a Professor of Mathematics at Auckland University of Technology. He received his PhD from The University of Auckland in 1999. He has published over 80 research articles in the areas of general topology, functional analysis, mathematical economics, and financial mathematics. He is a Fellow of the New Zealand Mathematics Society and holds visiting professorship positions at several other universities. From 2015 to present, he has been the Head of the Department of Mathematical Science at Auckland University of Technology.

Warren B. Moors is a Professor of Mathematics at the University of Auckland. He has published over 85 research articles in the areas of: functional analysis, general topology and optimisation. He is a Fellow of both the Australian Mathematical Society and the New Zealand Mathematical Society and is the recipient of the 2001 New Zealand Mathematical Society Research Award. He received his PhD from the University of Newcastle in 1992.