A metrization theorem for developable 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-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 note on dimension theory of metric 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 maximally resolvable spaces.
A note on metrics and tolerances
A note on operators extending partial ultrametrics
We consider the question of simultaneous extension of partial ultrametrics, i.e. continuous ultrametrics defined on nonempty closed subsets of a compact zero-dimensional metrizable space. The main result states that there exists a continuous extension operator that preserves the maximum operation. This extension can also be chosen so that it preserves the Assouad dimension.
A note on -spaces and -metrizable spaces
In this paper, we give the mapping theorems on -spaces and -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and -mappings.
A note on star Lindelöf, first countable and normal spaces
A topological space is said to be star Lindelöf if for any open cover of there is a Lindelöf subspace such that . The “extent” of is the supremum of the cardinalities of closed discrete subsets of . We prove that under every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under , which shows that a star Lindelöf, first countable and normal space may not have countable extent.
A note on -universal spaces
A perfectly normal locally metrizable non-paracompact space
A proof of the Moore metrization theorem
A property of semigroups on metric spaces.
A quasitopos containing CONV and MET as full subcategories.
A remark on R. G. Woods' paper "The minimum uniform compactification of a metric space" (Fund. Math. 147 (1995), 39–59)
A question raised in R. G. Woods' paper has a simple solution.