The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.

In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.

This thesis covers the Cantor Ternary Set and generalizations of the Cantor Set, and gives a complete existential theory for three set properties: denumerability, exhaustibility, and zero measure.

With the development of modern technology the perception of waste is changing. What was once considered unusable and expensive can be now seen as an useful material with potential to increase revenues of the company. As example can serve energetic industry, which was until recently only able to store its waste produced during combustion of coal. Now energetic companies are able to transform their waste into secondary energetic products (by-products) that can be further used in other industries. The main goal of the thesis is to determine whether there is a potential for the development of the secondary energetic products in the Czech Republic.