Compact and precompact sets in asymmetric locally convex spaces

S. Cobzas

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Compact and precompact sets in asymmetric locally convex spaces

机译：非对称局部凸空间中的紧和预紧集

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The aim of the present paper is to study precompactness and compactness within the framework of asymmetric locally convex spaces, defined and studied by the author in [S. Cobzas, Asymmetric locally convex spaces, Int. J. Math. Math. Sci. 2005 (16) (2005) 2585-2608]. The obtained results extend some results on compactness in asymmetric normed spaces proved by [L.M. Garcia-Raffi, Compactness and finite dimension in asymmetric normed linear spaces. Topology Appl. 153 (2005) 844-853], and [C. Alegre, I. Ferrando, L.M. Garcia-Raffi, E.A. Sanchez-Perez, Compactness in asymmetric normed spaces. Topology Appl. 155 (6) (2008) 527-539].

机译：本文的目的是研究非对称局部凸空间框架内的预紧性和紧致性。 Cobzas，非对称局部凸空间，Int。 J.数学数学。科学2005（16）（2005）2585-2608]。所获得的结果扩展了由[L.M. Garcia-Raffi，非对称赋范线性空间中的紧性和有限维。拓扑应用153（2005）844-853]和[C.阿莱格里（Alegre），费朗多（I. Sanchez-Perez，非对称赋范空间的紧致性。拓扑应用155（6）（2008）527-539]。

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来源
《Topology and its applications》 |2009年第9期|1620-1629|共10页
作者
S. Cobzas;
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作者单位

Babes-Bolyai University, Faculty of Mathematics and Computer Science, 400 084 Cluj-Napoca, Romania;

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正文语种 eng
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关键词
quasi-metric spaces; quasi-uniform spaces; spaces with asymmetric norm; asymmetric locally convex spaces; compactness; precompactness; total boundedness;

机译：准度量空间准均匀空间规范不对称的空间;不对称的局部凸空间;紧凑;预紧总边界;

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专利

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机译：紧凸集在局部凸空间中的嵌入
2. A short proof of Vladimirskii's theorem on precompact perturbations in locally convex spaces [J] . Canadian mathematical bulletin . 1975,第1975期

机译：关于局部凸空间中预紧摄动的弗拉基米尔斯基定理的简短证明
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机译：局部凸空间的不可度量紧凸空间的凸紧空间的超空间
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机译：非对称赋范空间中的弱凸集
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机译：关于局部凸向量空间中渐近紧集的Henig有效点的密度。
6. Theory of a Class of Locally Convex Vector Lattices Which Include the Lebesgue Spaces [O] . Witold M. Bogdanowicz 1970

机译：一类包括Lebesgue空间的局部凸向量格的理论
7. Compact and precompact sets in asymmetric locally convex spaces [O] . Cobzaş S. 2009

机译：非对称局部凸空间中的紧和预紧集
8. On the One-Skeleton of a Compact Convex Set in Banach Spaces. I [R] . Larman, D. G. 1973

机译：Banach空间中紧凸集的一个骨架。一世

Compact and precompact sets in asymmetric locally convex spaces

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