For many, modern functional analysis dates back to Banach's book Ba32]. Here, such powerful results as the Hahn-Banach theorem, the open-mapping theorem and the uniform boundedness principle were developed in the setting of complete normed and complete metrizable spaces. When analysts realized the power and applicability of these methods, they sought to generalize the concept of a metric space and to broaden the scope of these theorems. Topological methods had been generally available since the appearance of Hausdorff's book in 1914. So it is surprising that it took so long to recognize that...
For many, modern functional analysis dates back to Banach's book Ba32]. Here, such powerful results as the Hahn-Banach theorem, the open-mapping theo...
This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.
The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological...
This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of funct...
