A new characterization of spaces with locally countable -networks
A new class of quasi-uniform spaces.
A new look at pointfree metrization theorems
We present a unified treatment of pointfree metrization theorems based on an analysis of special properties of bases. It essentially covers all the facts concerning metrization from Engelking [1] which make pointfree sense. With one exception, where the generalization is shown to be false, all the theorems extend to the general pointfree context.
A new metrization theorem
We give a new metrization theorem on terms of a new structure introduced by the authors in [2] and called fractal structure. As a Corollary we obtain Nagata-Smirnovs and Uryshons metrization Theorems.
A non graph theory approach to Ulam's conjecture
A non-completely regular quiet quasi-metric.
A nondegenerate σ-discrete Moore space which is connected
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
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 metric in the group of reals
A nontransitive space based on combinatorics
Costruiamo uno spazio nontransitivo analogo al piano di Kofner. Mentre gli argomenti usati per la costruzione del piano di Kofner si fondano su riflessioni geometriche, le nostre prove si basano su idee combinatorie.
A non-zero dimensional atom
A non-zero dimensional atom in the lattice of uniformities
A note about -spaces and stratifiable spaces
A note on compact metric spaces as remainders.
A note on dimension theory of metric spaces
A note on D-spaces
Every semi-stratifiable space or strong -space has a -cushioned (mod)-network. In this paper it is showed that every space with a -cushioned (mod)-network is a D-space, which is a common generalization of some results about D-spaces.
A note on -metrizable spaces
In this paper, the relationships between metric spaces and -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
A note on k-c-semistratifiable spaces and strong -spaces
Recall that a space is a c-semistratifiable (CSS) space, if the compact sets of are -sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a -space is a k-c-semistratifiable space if and only if has a function which satisfies the following conditions: (1) For each , and for each . (2) If a...
A note on maximally resolvable spaces.