0
$\begingroup$

I encountered an example that said:

A Tychonoff 2-starcompact space of countable spread which is not $1\frac{1}{2}$-starcompact.

My question is this: What's the meaning of "countable spread" ?

  • 0
    Thanks for the books link, Martin Sleziak.2012-06-30

1 Answers 1

1

The question was answered in comments. Since we don't like leaving questions unanswered, I'll copy here the definitions from Wikipedia.

The cellularity of a space $X$ is ${\rm c}(X)=\sup\{|{\mathcal U}|:{\mathcal U}\text{ is a family of mutually disjoint non-empty open subsets of }X \}+\aleph_0.$

The hereditary cellularity (sometimes spread) is the least upper bound of cellularities of its subsets: $s(X)={\rm hc}(X)=\sup\{ {\rm c} (Y) : Y\subseteq X \}$ or $s(X)=\sup\{|Y|:Y\subseteq X \text{ with the subspace topology is discrete}\}+\aleph_0.$