Abstract
This chapter discusses spaces, mappings, and measures. Different classes of subsets of S are characterized by different set operations. A class G of subsets of S is called a σ-topological class of open sets if it is closed under countable unions and finite intersections and if S ∈ G, Ø ∈ G. The members of G are called open sets. If a σ-topological class of open sets is closed under arbitrary unions, it is called a topological class of open sets, and if a σ-topological class of closed sets is closed under arbitrary intersections, it is called a topological class of closed sets. A class S of subsets of a set S is called a Boolean algebra. A set S together with a σ-topological class of closed subsets of S is said to form a σ-topological space. If an A-space is second-order countable, it is a topological space.
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