Abstract
This chapter discusses some questions about properties defined in terms of stars with respect to open covers. If u is a cover of X, and A a subset of X, then St(A, u) =St1(A, u) = U{U ∈u : U ∩ A ≠ Ø ;}. For n =1, 2, . , Stn+1(A, u) =St(Stn(A, u), u). Even if many properties can be characterized in terms of stars and normality is equivalent to the requirement that every finite open cover has an open star refinement, the discussion focuses mostly on properties specifically defined by means of stars. All spaces are assumed to be Tychonoff unless a weaker axiom of separation is indicated. If A is an almost disjoint family of infinite subsets of ω, then Ψ (A) denotes the associated Ψ‑space. The chapter describes in detail the concepts related to compactness-type properties. It details about Lindelöf-type properties and cardinal functions. Concepts of paracompactness-type properties are also explained in the chapter.
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