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Start Over Subject Urysohn space

1. Extension and reconstruction theorems for the Urysohn universal metric space

Creator:
Kubiś, Wiesław and Rubin, Matatyahu
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Urysohn space, bilipschitz homeomorphism, modulus of continuity, reconstruction theorem, and extension theorem
Language:
English
Description:
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On dense subspaces satisfying stronger separation axioms

Creator:
Alas, Ofelia Teresa, Tchakenko, Mihail G., Tkachuk, Vladimir Vladimirovich, Wilson, Richard Gordon, and Yashchenko, Ivan V
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hausdorff space, Urysohn space, completely Hausdorff space, and filter of dense sets
Language:
English
Description:
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than $c$ has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight $c$ which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of $\pi$-weight less than $\mathfrak p$ has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without “good” dense subsets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public