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Contractions of Nadler type on partial tvs-cone metric spaces

100%

Ge X., Lin S.

Colloquium Mathematicum

2015

tom 138

nr 2

149-163

This paper introduces partial tvs-cone metric spaces as a common generalization of both tvs-cone metric spaces and partial metric spaces, and gives a new fixed point theorem for contractions of Nadler type on partial tvs-cone metric spaces. As corollaries, we obtain the main results of S. B. Nadler (1969), D. Wardowski (2011), S. Radenović et al. (2011) and H. Aydi et al. (2012) are deduced.

A note on pseudobounded paratopological groups

81%

Lin F., Lin S., Sánchez I.

Topological Algebra and its Applications

2014

tom 2

nr 1

Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if for every neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn). We show that every feebly compact (2-pseudocompact) pseudobounded (ω-pseudobounded) premeager paratopological group is a topological group. Also,we prove that if G is a totally ω-pseudobounded paratopological group such that G is a Lusin space, then is G a topological group. We present some examples of paratopological groups with interesting properties: (1) There exists a metrizable, zero-dimensional and pseudobounded topological group; (2) There exists a Hausdorff ω-pseudobounded paratopological group G such that G contains a dense subgroup which is not ω-pseudobounded; (3) There exists a Hausdorff connected paratopological group which is not ω-pseudobounded.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Topological Algebra and its Applications

2 Lin S.

1 Ge X.

1 Lin F.

1 Sánchez I.

1 2015

1 2014

Wyniki wyszukiwania

Contractions of Nadler type on partial tvs-cone metric spaces

A note on pseudobounded paratopological groups