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 new way to find compact zero-dimensional first countable preimages of first countable compact spaces
A non-metrizable collectionwise Hausdorff tree with no uncountable chains and no Aronszajn subtrees
It is independent of the usual (ZFC) axioms of set theory whether every collectionwise Hausdorff tree is either metrizable or has an uncountable chain. We show that even if we add “or has an Aronszajn subtree,” the statement remains ZFC-independent. This is done by constructing a tree as in the title, using the set-theoretic hypothesis , which holds in Gödel’s Constructible Universe.
A non-Standard Characterization of the norm of free Ultrafilters
A Note on Alpha-equivalent Topologies
A note on cardinal invariants of square
A note on condensations of onto compacta
A condensation is a one-to-one continuous mapping onto. It is shown that the space of real-valued continuous functions on in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum (Theorem 19). However, there exists a non-metrizable compactum such that condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated.
A note on connectedness in intuitionistic fuzzy special topological spaces.
A note on dense subspaces of dyadic compact spaces
A note on diagonal and matrix properties of convergence spaces
A note on discrete sets
We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.
A note on discretely absolutely star-Lindelöf spaces
A note on extremally disconnected frames
A note on generalized Souslin's problem
A note on inverse-preservations of regular open sets.
A note on maximally resolvable spaces.
A note on neighborhood product spaces
A note on pretopologies
A note on products of Fréchet spaces
A note on pseudobounded paratopological groups
Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group....