When is \(|C(X\times Y)|= |C(X)||C(Y)|\)? (Q2716493)
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scientific article; zbMATH DE number 1599063
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | When is \(|C(X\times Y)|= |C(X)||C(Y)|\)? |
scientific article; zbMATH DE number 1599063 |
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1 February 2002
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product
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cardinalities
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real-valued functions
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0.81001914
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0.80407345
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0.79790926
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0.7859416
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0.7805857
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When is \(|C(X\times Y)|= |C(X)||C(Y)|\)? (English)
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It is clear, given two spaces \(X\) and \(Y\), that \(|C(X\times Y)|\geq|C(X)||C(Y)|\), hence the question in the title. The authors give a lot of conditions for the equality to hold, most in terms of relations between well-known cardinal functions like density and cellularity. They also present examples where inequality obtains, including for every~\(n\) spaces~\(X\) with \(|C(X^k)|={\mathfrak c}\) for \(k\leq n\) and \(|C(X^k)|=2^{\mathfrak c}\) for \(k>n\).
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