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

الموضوعات :

M. Rahimi ¹ (I. A. U. Aligudarz Branch, Department of Mathematics, Aligudarz, Iran)
S. M. Vaezpour ² (Dept. of Math., Amirkabir University of Technology, Hafez Ave, Tehran, Iran)

تاريخ الإرسال : 17 السبت , ذو الحجة, 1435 تاريخ التأكيد : 03 الخميس , ربيع الأول, 1436 تاريخ الإصدار : 07 الإثنين , ربيع الأول, 1436

الکلمات المفتاحية: Locally convex space, Minkowski functional, Topological number,

ملخص المقالة :

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

المصادر:

[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.