Regarding a question about the least element map
Relations between ß X / X and a Certain Subspace of ... X.
Remarks on absolutely star countable spaces
We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which...
Resolving a question of Arkhangel'skiĭ's
We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Results and problems concerning compactifications, compact subtopologies, and mappings
Rudin's Dowker space in the extension with a Suslin tree
We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced...
Small subsets of first countable spaces
Some counterexamples and properties on generalizations of Lindelöf spaces.
Some examples in the dimension theory of Tychonoff spaces
Some examples related to colorings
We complement the literature by proving that for a fixed-point free map the statements (1) admits a finite functionally closed cover with for all (i.e., a coloring) and (2) is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitted. We also show that a theorem due to van Mill is sharp: for every we construct a strongly zero-dimensional Tychonov space...
Some m-dimensional compacta admitting a dense set of imbeddings into
Some Remarks On Choice Topology
Some remarks on choice topology.
Spaces with zero set bases
Stationary sets, trees and continuums.
Strongly irresolvable spaces.
Sum theorems for Ohio completeness
We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.
The Arkhangel’skiĭ–Tall problem: a consistent counterexample
We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.
The box product of countably many metrizable spaces need not be normal
The dimension of products of complete separable metric spaces