On Several Cardinality Bounds on Power Homogeneous Spaces
by
Nathan Carlson
California Lutheran University
Coauthors: Guit-Jan Ridderbos

We show the cardinality of a homogeneous Hausdorff space X is not necessarily bounded by 2^L(X)pc(X) by providing examples of s-compact, countably tight, homogeneous spaces of countable p-character and arbitrary cardinality. We also generalize a closing-off argument of Pytkeev to show the cardinality of any power homogeneous Hausdorff space X is at most 2^{L(X)pct(X)t(X)}. This was previously shown to hold if X is also regular by G.J. Ridderbos. Another consequence of the generalization of Pytkeev's closing-off argument is the well-known cardinality bound 2^L(X)t(X)y(X) for an arbitrary Hausdorff space X.

Date received: December 24, 2009