ORDER-THEORETIC INVARIANTS IN SET-THEORETIC TOPOLOGY (original) (raw)

We present several results related to van Douwen's Problem, which asks whether there is homogeneous compactum with cellularity exceeding c, the cardinality of the reals. For example, just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Peregudov's Noetherian type and related cardinal functions defined by order-theoretic base properties. Also, assuming GCH, every point in a homogeneous compactum X has a local base in which every element has fewer supersets than the cellularity of X.