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Some properties of rectifiable spaces

100%

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.

Ordered spaces with special bases

72%

Bennett H. R. , Lutzer D. J.

Fundamenta Mathematicae

1998

tom 158

nr 3

289-299

We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a $G_δ$-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.

Regular covers and metrization

58%

Lin S.

2002

tom Vol. 50, no 4

427-432

In this paper it is showed that a regular and k-space with a regular k-network is metrizable, which generalized related results of A. Archangielskiĭ, H. W. Martin, M. Sakai, K. Tamano and Y. Yajima.

Convergence in measure through compactifications

58%

Wajch E.

2016

tom Y. 113, iss. 1-NP

137--145

For a metrizable space X, concepts of metric convergence in measure and of functional convergence in measure of sequences of measurable mappings taking their values in X are introduced and applied to a comparison of compactifications of X.

Dla przestrzeni metryzowalnej X, wprowadza się pojęcia metrycznej zbieżności według miary i funkcyjnej zbieżności według miary ciągów odwzorowań mierzalnych, przyjmujących swe wartości w X oraz stosuje się te pojęcia do porównywania uzwarceń przestrzeni X.

Uniform properties and hyperspaces of metrizable spaces

44%

Costantini C. , Vitolo P.

Journal of Applied Analysis

1999

tom Vol. 5, nr 2

187-196

Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.