Separation in sequential spaces under PMEA
Separation properties in Moore spaces
Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems [Book]
Sixty questions on regular not paracompact spaces
Some characterization of c-paracompact and c-collectionwise normal spaces by continuous selections (II).
Some characterizations of c-paracompact and c-collectionwise normal spaces by continuous selections (I).
In this note we characterize the c-paracompact and c-collectionwise normal spaces in terms of continuous selections. We include the usual techniques with the required modifications by the cardinality.
Some continuous separation axioms
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 factorization theorems for closed subspaces
Some generalizations of completely normal spaces
Some more -fully normal spaces
Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane
We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey plane...
Some remarks about bijections onto metric spaces
Some results on expansions for normal and completely normal spaces.
Some topological consequences of the Product Measure Extension Axiom
Some topological properties weaker than Lindelofness
Spaces for which the diagonal has a closed neighborhood base
Spaces of continuous functions, -products and Box Topology
For a Tychonoff space , we will denote by the set of its isolated points and will be equal to . The symbol denotes the space of real-valued continuous functions defined on . is the Cartesian product with its box topology, and is with the topology inherited from . By we denote the set can be continuously extended to all of . A space is almost--resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of has a non-empty...
Spaces with a binary normal subbase