Metrizability and weight of inverses under confluent mappings
Metrizability, generalized metric spaces and -functions
Metrizability of certain Pixley-Roy spaces
Metrizability of inverse images of metric spaces under open perfect and 0-dimensional mappings
Metrizability of spaces with countably based closed sets
Metrizability of trees
Metrizability of -frames
Metrizabillity of certain quotient space
Metrizable subsets of Moore spaces
Metrization criteria for compact groups in terms of their dense subgroups
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...
Metrization of Compact Convex Sets.
Metrization of function spaces with the Fell topology
For a Tychonoff space , let be the family of hypographs of all continuous maps from to endowed with the Fell topology. It is proved that has a dense separable metrizable locally compact open subset if is metrizable. Moreover, for a first-countable space , is metrizable if and only if itself is a locally compact separable metrizable space. There exists a Tychonoff space such that is metrizable but is not first-countable.
Metrization of Moore spaces and generalized manifolds
Metrization of Quasi-Metric Spaces.
Metrization of uniform lattices
Metrization, paracompactness, and real-valued functions
Metrization, paracompactness, and real-valued functions II
Mildly (-normal spaces and some bitopological functions
The aim of the paper is to introduce and study a new class of spaces called mildly -normal spaces and a new class of functions called --continuous, --map, almost -continuous function and almost --closed function in bitopological spaces. Subsequently, the relationships between mildly -normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly -normal spaces, properties of the new bitopological functions and preservation theorems for...
Minimal bi-Lipschitz embedding dimension of ultrametric spaces
We prove that an ultrametric space can be bi-Lipschitz embedded in if its metric dimension in Assouad’s sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
Minimal points in product spaces.