A characterization of Hurewicz spaces
A characterization of paracompactness
A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
A class of spaces whose Cartesian product with every hereditarily Lindelöf space in Lindelöf
A Classification Of Topological Spaces. Z-Number Of Spaces
A compact Hausdorff topology that is a T₁-complement of itself
Topologies τ₁ and τ₂ on a set X are called T₁-complementary if τ₁ ∩ τ₂ = X∖F: F ⊆ X is finite ∪ ∅ and τ₁∪τ₂ is a subbase for the discrete topology on X. Topological spaces and are called T₁-complementary provided that there exists a bijection f: X → Y such that and are T₁-complementary topologies on X. We provide an example of a compact Hausdorff space of size which is T₁-complementary to itself ( denotes the cardinality of the continuum). We prove that the existence of a compact Hausdorff...
A construction of a Fréchet-Urysohn space, and some convergence concepts
Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen mapping....
A Corson compact L-space from a Suslin tree
The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.
A countably compact, separable space which is not absolutely countably compact
We construct a space having the properties in the title, and with the same technique, a countably compact topological group which is not absolutely countably compact.
A Dowker group
A few topological problems
A function space C(X) which is weakly Lindelöf but not weakly compactly generated
A game and its relation to netweight and D-spaces
We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Lindelöf spaces are shown.
A generic theorem in the theory of cardinal invariants of topological spaces
Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.
A lattice of conditions on topological spaces II
A lemma on finite-dimensional covers
A Lindelöf space X such that is normal but not paracompact
A local-nonglobal Hurewicz fibration
A new Lindelöf space with points
We prove that implies there is a zero-dimensional Hausdorff Lindelöf space of cardinality which has points . In addition, this space has the property that it need not be Lindelöf after countably closed forcing.
A note on Ascol's theorem for spaces of multifunctions.