Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: filters

Sortuj według:

Ogranicz wyniki do:

Filters and sequences

100%

Solecki S.

Fundamenta Mathematicae

2000

tom 163

nr 3

215-228

We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a $Π^0_3$ filter is itself $Π^0_3$ and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou's lemma.

Summable Family in a Commutative Group

75%

Coghetto R.

Formalized Mathematics

2015

tom 23

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.

Ograniczanie wyników

1 Formalized Mathematics

1 Fundamenta Mathematicae

1 Coghetto R.

1 Solecki S.

1 2015

1 2000

Wyniki wyszukiwania

Filters and sequences

Summable Family in a Commutative Group