EuDML | Browse

A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, $U_{α} : α \in ℕ^{ℕ}$ , such that $U_{α} \subset U_{β}$ whenever β ≤ α for all $α, β \in ℕ^{ℕ}$ . The class of all metrizable topological groups is a proper subclass of the class $T G_{}$ of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group $G \in T G_{}$ is metrizable, and hence G is strictly angelic. We deduce from this result...

On topologies of free groups

Mihail G. Tkachenko (1984)

Czechoslovak Mathematical Journal

On totally non-commutative convergence groupoids

Ján Šipoš (1989)

Mathematica Slovaca

On unitary Cauchy filters on topological monoids

Boris G. Averbukh (2013)

Topological Algebra and its Applications

For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose...

On unitary extensions and unitary completions of topological monoids

Boris G. Averbukh (2016)

Topological Algebra and its Applications

The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.

On universal enveloping algebras in a topological setting

Daniel Beltiţă, Mihai Nicolae (2015)

Studia Mathematica

We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...

On weakly almost periodic sets.

W. Ruppert (1985)

Semigroup forum

On zero-dimensionality of subgroups of locally compact groups

Dmitriĭ B. Shakhmatov (1991)

Commentationes Mathematicae Universitatis Carolinae

Improving the recent result of the author we show that $ind H = 0$ is equivalent to $dim H = 0$ for every subgroup $H$ of a Hausdorff locally compact group $G$ .

On $α$ -level topological groups.

Salih, Haval Mahmood Mahamad, Borumand Saeid, Arsham (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

One-parameter submonoids in locally complete differentiable monoids

Mitch Anderson (1980)

Colloquium Mathematicae

Open mapping theorems in topological spaces

Dominik Noll (1985)

Czechoslovak Mathematical Journal

Open subgroups and Pontryagin duality.

W. Banaszczyk, M.J. Chasco (1994)

Mathematische Zeitschrift

Open subgroups of free topological groups

Jeremy Brazas (2014)

Fundamenta Mathematicae

The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.

Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh, Svetlana Dimitrova (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its Stone-Čech compactification $β S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f : S \to Y$ to a second countable space $Y$ can be written as the composition $f = g \circ p$ of an open map $p : X \to Z$ onto a second countable space $Z$ and a map $g : Z \to Y$ . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.

Orbit projections of proper Lie groupoids as fibrations

Armin Rainer (2009)

Czechoslovak Mathematical Journal

Let $𝒢 ⇉ M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M / 𝒢$ is a fibration if and only if $𝒢 ⇉ M$ is regular.

Currently displaying 521 – 540 of 925

Previous Page 27 Next