Master’s thesis is devoted to the study of cardinal invariants in the F-compact spaces class. Here and throughout the paper, the concept ”compact” would mean a compact Hausdorff space. In my thesis I have tried to present and explain all necessary concepts and statements necessary for the reader to get acquainted with F-compact spaces class. In order to understand the idea of F-compact spaces, it is necessary to understand what the inverse spectrum is from itself, it is necessary to know about the cardinality of sets and to understand that two infinite sets can have different cardinalities, know about closed and open sets, and much else that you will find in this paper. In the thesis the analysis of the scientific literature sources is presented; the theorems about the relationship between the characteristics of cardinality invariants in the F-compact spaces class are investigated; the relationships between the properties of perfect normality and hereditary normality in the F - compact spaces class of countable spectral height are studied. In the process of the investigation some propositions were found, proved and filled in the missing fragments of evidence. Conclusion: At present, the method of fully closed mappings (which is used in constructing of F - compact spaces ) is the most productive method of constructing counterexamples in general topology. I believe, that this paper will be interesting to all who wants to go beyond the ordinary, habitual way of thinking, because only by studying topology we can speak clearly and precisely about things related to the idea of continuity and infinity!

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