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- W1966292717 abstract "This expository paper describes a number of theorems dealing with cardinal numbers associated with topoligical spaces. The weight, density character, and cellular number receive chief attention. A few of the theorems cited-e.g., the Hewitt-Pondionery-Marczewski theorem on the density character of a product space, and the Erdös-Tarski theorem asserting that the cellular number, unless uncountable and weakly inaccessible, is achieved — has been known for many years; proofs are included. Other equally exciting results of more recent vintage, such as Arhangel'skii's solution to the Alexandroff problem, the Hajnal-Jokise evaluation of the number of sets in a Hausdorff topology, and Nyiko's solution to the Engelking-Mröwka problem, have perhaps not yet achieved their optimal statement and/or proof, these results are stated here as carefully and completely as time and the present author's ability permit, but the proofs are only sketched, or omitted entirely. The following also are briefly mentioned: Smirnov's theorem w(ßX) = C∗(X); the F.K. Schmidt A.H. Stone-Kruse theorem |C(X)|=|C(X)|ℵ0; the relation ml = m in Stonian spaces; the Noble-Ulmer cluster of theorems on preservation of certain cardinal properties under passage to products; and Mrówka's theorems on embedding the discrete space D(m) as a closed subspace of Nm." @default.
- W1966292717 created "2016-06-24" @default.
- W1966292717 creator A5003826957 @default.
- W1966292717 date "1971-08-01" @default.
- W1966292717 modified "2023-09-27" @default.
- W1966292717 title "A survey of cardinal invariants" @default.
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- W1966292717 doi "https://doi.org/10.1016/0016-660x(71)90122-x" @default.
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