All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2

Displaying 21 – 37 of 37

Showing per page

On topological and algebraic structure of extremally disconnected semitopological groups

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order 2 . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...

Pseudoradial Spaces: Finite Products and an Example From CH

Simon, Petr, Tironi, Gino (1998)

Serdica Mathematical Journal

∗ The first named author’s research was partially supported by GAUK grant no. 350, partially by the Italian CNR. Both supports are gratefully acknowledged. The second author was supported by funds of Italian Ministery of University and by funds of the University of Trieste (40% and 60%).Aiming to solve some open problems concerning pseudoradial spaces, we shall present the following: Assuming CH, there are two semiradial spaces without semi-radial product. A new property of pseudoradial spaces...

Remarks on extremally disconnected semitopological groups

Igor V. Protasov (2002)

Commentationes Mathematicae Universitatis Carolinae

Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

The Golomb space is topologically rigid

Taras O. Banakh, Dario Spirito, Sławomir Turek (2021)

Commentationes Mathematicae Universitatis Carolinae

The Golomb space ℕ τ is the set ℕ of positive integers endowed with the topology τ generated by the base consisting of arithmetic progressions { a + b n : n ≥ 0 } with coprime a , b . We prove that the Golomb space ℕ τ is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.

Topologies on groups determined by right cancellable ultrafilters

Igor V. Protasov (2009)

Commentationes Mathematicae Universitatis Carolinae

For every discrete group G , the Stone-Čech compactification β G of G has a natural structure of a compact right topological semigroup. An ultrafilter p ∈ G * , where G * = β G ∖ G , is called right cancellable if, given any q , r ∈ G * , q p = r p implies q = r . For every right cancellable ultrafilter p ∈ G * , we denote by G ( p ) the group G endowed with the strongest left invariant topology in which p converges to the identity of G . For any countable group G and any right cancellable ultrafilters p , q ∈ G * , we show that G ( p ) is homeomorphic to G ( q ) if and only if...

Two-fold theorem on Fréchetness of products

Szymon Dolecki, Tsugunori Nogura (1999)

Czechoslovak Mathematical Journal

A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.

Undetermined sets of point-open games

Janusz Pawlikowski (1994)

Fundamenta Mathematicae

We show that a set of reals is undetermined in Galvin's point-open game iff it is uncountable and has property C", which answers a question of Gruenhage.

Currently displaying 21 – 37 of 37

Previous Page 2