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Topological Rough Groups

Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan (2016)

Topological Algebra and its Applications

The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.

Topological type of weakly closed subgroups in Banach spaces

Tadeusz Dobrowolski, Janusz Grabowski, Kazuhiro Kawamura (1996)

Studia Mathematica

The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in 1 which are interesting from the Banach space theory point of view are discussed.

Topology of the isometry group of the Urysohn space

Julien Melleray (2010)

Fundamenta Mathematicae

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise, the group...

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