Topological number for locally convex topological spaces with continuous semi-norms

Journal of Linear and Topological Algebra

مقاله 3، دوره 03، شماره 03، آذر 2014، صفحه 149-158   

نویسندگان

M. Rahimi^{* 1}؛ S. M. Vaezpour²

¹I. A. U. Aligudarz Branch, Department of Mathematics, Aligudarz, Iran

²Dept. of Math., Amirkabir University of Technology, Hafez Ave, Tehran, Iran

چکیده

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

کلیدواژه‌ها

Locally convex space؛ Minkowski functional؛ Topological number

مراجع

[1] H. Brezis, Analysis Fonctionelle: Theorie et Applications, Dunod Dalloz Masson 34 Diffuseur, 2002.

 

[2] N. Bourbaki, Spaces Vectorials Topologiques, Paris, Hermann, 1967.

 

[3] J. B. Conway, A Course in Functional Analysis, Springer-Verlag, 1994.

 

[4] C. Lixing, Z. Yunchi and Z. Fong, Danes Drop theorem in locally convex spaces, Proc. Amer. Math. Soc, 124(12)(1996), 3699-3702.

 

[5] P. Robertson, W. Robertson, Topological vector spaces, Cambridge University, 1966.

 

[6] H. Shaferr, Topological vector spaces, New York:Springer-Verlag, 1971.

 

[7] R. Tyrrell and R. Fellar, Convex Analysis, Princeton University Press, 1970.

 

[8] E. Zeidler, Applied functional analysis, Main principles and their application, Contents of AMS, Volume 109, Springer Verlag, 1995.