Wyniki wyszukiwania - Biblioteka Nauki

Ten serwis zostanie wyłączony 2025-02-11.

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 7

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: topological group

Sortuj według:

Ogranicz wyniki do:

Examples of sequential topological groups under the continuum hypothesis

100%

Shibakov A.

nr 2

107-120

Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and $α_1$ topological group which contains no copy of the rationals.

Some properties of rectifiable spaces

88%

Tuyen L. Q. , Tuyen O. N.

2018

tom Nr 60

181--190

In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.

Uniform Space

75%

Coghetto R.

nr 3

215-226

In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation. Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\A) × (X\A)) ∪ (A×A) is presented.

Almost all submaximal groups are paracompact and σ-discrete

75%

Alas O. T. , Protasov I. V. , Tkačenko M. G. , Tkachuk V. V. , Wilson R. G. , Yaschenko I. V.

nr 3

241-260

We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.

Summable Family in a Commutative Group

75%

Coghetto R.

nr 4

279-288

Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [22], [7]. In this paper we present our formalization of this theory in Mizar [6]. First, we compare the notions of the limit of a family indexed by a directed set, or a sequence, in a metric space [30], a real normed linear space [29] and a linear topological space [14] with the concept of the limit of an image filter [16]. Then, following Bourbaki [9], [10] (TG.III, §5.1 Familles sommables dans un groupe commutatif), we conclude by defining the summable families in a commutative group (“additive notation” in [17]), using the notion of filters.

Measures in locally compact groups are carried by meager sets

63%

Zakrzewski P. , Zindulka O.

tom Vol. 7, nr 2

225-233

We show that for a σ-finite diffused Borel measure in a nondiscrete locally bounded topological group there is a meager set whose complement is of measure zero.

Group structures and rectifiability in powers of spaces

63%

Ridderbos G. J.

2007

tom Vol. 55, no 4

357-363

We prove that if some power of a space X is rectiflable, then X[sup]πω(x) is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangeliskiî. We also show that in Mal'tsev spaces of point-countable type, character and π-character coincide.