There is no universal separable Fréchet or sequential compact space
There is no universal totally disconnected space
Three countable connected spaces
Three results on I-sets
Three small results on normal first countable linearly H-closed spaces
We use topological consequences of PFA, MA(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.
Three technical tools in uniform spaces
Three Theorems on ...-m-Expandable Spaces.
Tightness and π-character in centered spaces
We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered...
Tightness of compact spaces is preserved by the -equivalence relation
We prove that if there is an open mapping from a subspace of onto , then is a countable union of images of closed subspaces of finite powers of under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if and are -equivalent compact spaces, then and have the same tightness, and that, assuming , if and are -equivalent compact spaces and is sequential, then is sequential.
Topological and Algebraic Copies of in .
Topological compactifications
We study those compactifications of a space such that every autohomeomorphism of the space can be continuously extended over the compactification. These are called H-compactifications. Van Douwen proved that there are exactly three H-compactifications of the real line. We prove that there exist only two H-compactifications of Euclidean spaces of higher dimension. Next we show that there are 26 H-compactifications of a countable sum of real lines and 11 H-compactifications of a countable sum of Euclidean...
Topological completeness of first countable Hausdorff spaces II
Topological completeness of first countable Hausdorff spaces I
Topological Continuous Convergence.
Topological extensions and subspaces of -sets
Topological games and product spaces
In this paper, we deal with the product of spaces which are either -spaces or -spaces, for some . These spaces are defined in terms of a two-person infinite game over a topological space. All countably compact spaces are -spaces, and every -space is a -space, for every . We prove that if is a set of spaces whose product is a -space, then there is such that is countably compact for every . As a consequence, is a -space iff is countably compact, and if is a -space, then all...
Topological games and products I
Topological games and products, II
Topological games and products, III
Topological open problems in the geometry of Banach spaces.