Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Separable extensions of first countable spaces
Sequential + separable vs sequentially separable and another variation on selective separability
A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.
Small subsets of first countable spaces
Spaces with a locally countable -network.
Spaces with countable -networks
In this paper, we prove that a space is a sequentially-quotient -image of a metric space if and only if has a point-star -network consisting of -covers. By this result, we prove that a space is a sequentially-quotient -image of a separable metric space if and only if has a countable -network, if and only if is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...
Spaces with --linked topologies as special subspaces of separable spaces
We characterize spaces with --linked bases as specially embedded subspaces of separable spaces, and derive some corollaries, such as the -productivity of the property of having a -linked base.
Stationary sets, trees and continuums.
The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to linear isometry....
True preimages of compact or separable sets for functional analysts
We discuss various results on the existence of ‘true’ preimages under continuous open maps between -spaces, -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
Tychonoff products of super second countable and super separable metric spaces
Weak selections and weak orderability of function spaces
It is proved that for a zero-dimensional space , the function space has a Vietoris continuous selection for its hyperspace of at most 2-point sets if and only if is separable. This provides the complete affirmative solution to a question posed by Tamariz-Mascarúa. It is also obtained that for a strongly zero-dimensional metrizable space , the function space is weakly orderable if and only if its hyperspace of at most 2-point sets has a Vietoris continuous selection. This provides a partial...
-continuity between two pointwise quasi-uniformity spaces.
О связи между деревьями Ароншайна и неметризуемыми aleph//0-монолитными линейно упорядоченными бикомпактами, удовлетворяющими первой аксиоме счетности
Универсальные элементы для семейств сепарабельных метрических пространств