doc. RNDr. Zdeněk Mihula, Ph.D.

Varied arguments resting on compactness of some sets in function spaces, which are usually infinite dimensional, play important roles in various parts of mathematics, such as analysis of partial differential equations or variational problems. Much as compactness is useful, it is not always at our disposal. Nevertheless, even without compactness, it is sometimes possible to somehow compensate for it, which usually requires very fine-grained analysis of the problem. The ultimate goal of the thesis is to study some open problems in the analysis of compactness and noncompactness and, ideally, to solve them, or at least to achieve some substantial advancements. The language of the thesis is English.