O riešení niektorých nerozhodnutelných topologických problémov
Observations on spaces with zeroset or regular -diagonals
We show that if has countable extent and has a zeroset diagonal then is submetrizable. We also make a couple of observations regarding spaces with a regular -diagonal.
Omitting cardinals in tame spaces
On a cardinal invariant resembling the Souslin number
On a condition for the pseudo radiality of a product
A sufficient condition for the pseudo radiality of the product of two compact Hausdorff spaces is given.
On a problem of Sikorski
On a theorem of Jones and Heath concerning separable normal spaces
On a theorem of Šapirovskiĭ on the size of a sequential space.
On cardinalities of row spaces of Boolean matrices.
On -chain-net spaces.
On character and chain conditions in images of products
A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property which we show is satisfied by all ξ-adic spaces. Whereas Property is productive, we show that a weaker (but more natural) Property is not productive. Polyadic...
On closed inverse images of base-paracompact spaces.
On compact spaces carrying Radon measures of uncountable Maharam type
If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable space, then there is a continuous surjection from X onto .
On compact spaces carrying random measures of large Maharam type
On compact spaces which are unions of certain collections of subspaces of special type. II.
On compact spaces which are unions of certain collections of subspaces of special type
On compactness with respect to semi-open sets
On countable Fréchet-Urysohn spaces
On D-dimension of metrizable spaces
For every cardinal τ and every ordinal α, we construct a metrizable space and a strongly countable-dimensional compact space of weight τ such that , and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of and to a subspace of .
On decomposition of spaces on meager sets