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 3 Next

Displaying 41 – 60 of 351

Showing per page

On a theorem of W.W. Comfort and K.A. Ross

Aleksander V. Arhangel'skii (1999)

Commentationes Mathematicae Universitatis Carolinae

A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is C -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group G and prove that every G δ -dense subspace Y of a topological group G , such...

On a universality property of some abelian Polish groups

Su Gao, Vladimir Pestov (2003)

Fundamenta Mathematicae

We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.

On a weak form of uniform convergence

Jaroslav Fuka, Petr Holický (2005)

Commentationes Mathematicae Universitatis Carolinae

The notion of Δ -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces X for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on X implies Δ -convergence are σ -compact spaces. We show that the assumption...

On absolute stability

Roger C. McCann (1972)

Annales de l'institut Fourier

Absolute stability of a compact set is characterized by the cardinality of a fundamental system of positively invariant neighborhoods.

On analyticity in cosmic spaces

Oleg Okunev (1993)

Commentationes Mathematicae Universitatis Carolinae

We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a K -analytic space under a measurable mapping. We also obtain characterizations of analyticity and σ -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if X is a separable metrizable space and Y is its dense subspace then the space of restricted continuous functions C p ( X ∣ Y ) is analytic iff it is a K σ δ -space iff X is σ -compact.

On approximation of homeomorphisms of a Cantor set

Konstantin Medynets (2007)

Fundamenta Mathematicae

We continue the study of topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ, which was started by Bezuglyi, Dooley, Kwiatkowski and Medynets. We prove that the set of periodic homeomorphisms is τ-dense in Homeo(X) and deduce from this result that the topological group (Homeo(X),τ) has the Rokhlin property, i.e., there exists a homeomorphism whose conjugacy class is τ-dense in Homeo(X). We also show that for any homeomorphism...

On B -spaces

Zdeněk Frolík (1968)

Commentationes Mathematicae Universitatis Carolinae

Currently displaying 41 – 60 of 351