289 research outputs found
The Solecki submeasures and densities on groups
We introduce the Solecki submeasure and its left and right modifications on a group , and study the
interplay between the Solecki submeasure and the Haar measure on compact
topological groups. Also we show that the right Solecki density on a countable
amenable group coincides with the upper Banach density which allows us to
generalize some fundamental results of Bogoliuboff, Folner, Cotlar and
Ricabarra, Ellis and Keynes about difference sets and Jin, Beiglbock, Bergelson
and Fish about the sumsets to the class of all amenable groups.Comment: 34 page
Categorically closed topological groups
Let be a subcategory of the category of topologized semigroups
and their partial continuous homomorphisms. An object of the category
is called -closed if for each morphism
of the category the image is closed in . In the paper
we detect topological groups which are -closed for the categories
whose objects are Hausdorff topological (semi)groups and whose
morphisms are isomorphic topological embeddings, injective continuous
homomorphisms, continuous homomorphisms, or partial continuous homomorphisms
with closed domain.Comment: 26 page
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