Document Type: Research Paper

Authors

1 Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

2 Punjab Education Department, Pakistan

Abstract

In this paper, we have de ned and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are de ned by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is an s-topological vector space. A homomorphism between s-topological vector spaces is semi-continuous if it is s-continuous at the identity.

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Main Subjects

###### ##### References

[1] S. M. Alsulami and L. A. Khan, Weakly Almost Periodic Functions in Topologicl Vector Spaces, Afr. Diaspora J. Math.. (N.S.), 15(2)(2013), 76-86.

[2] G. Bosi, J.C. Candeal,; E. Indurain,; M. Zudaire, Existence of Homogenous Representations of interval Orders on a Cone in Topological Vector Space, Social Choice and welfare, Vol.24 (2005), 45-61.

[3] D. E. Cameron and G. Woods, s-Continuous and s-Open Mappings, preprint.

[4] Y. Q. Chen, Fixed Points for Convex Continuous mappings in Topological Vector Space, American Mathematical Society, Vol. 129 (2001), 2157-2162.

[5] S. T. Clark, A Tangent Cone Analysis of Smooth Preferences on a Topological Vector Space, Economic Theory, Vol.23 (2004), 337-352.

[6] S. G. Crossley, S.K. Hildebrand, Semi-closed sets and semi-continuity in topological spaces, Texas J. Sci., Vol. 22 (1971), 123-126.

[7] S. G. Crossley, S.K. Hildebrand, Semi-closure, Texas J. Sci. 22 (1971), 99-112.

[8] S. G. Crossley, S.K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.

[9] L. Drewnowski, Resolution of topological linear spaces and continuity of linear maps., Anal. Appl. 335 (2) (2007), 1177-1195.

[10] A. Grothendieck. Topological vector spaces. New York: Gordon and Breach Science Publishers, (1973).

[11] D. H. Hyers, Pseudo-normed linear spaces and Abelian groups, Duke Mathematical Journal, Vol. 5 (1939), 628-634.

[12] J. L. Kelly, General topology, Van Nastrand (New York 1955).

[13] Kolmogro , Zur Normierbarkeit eines topologischen linearen Raumes, Studia Mathematica, Vol. 5 (1934), 29-33.

[14] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, Vol. 70 (1963), 36-41.

[15] J. V. Neuman, On complete topological spaces, Transactions of American Mathematical Society, Vol. 37 (1935), 1-2.

[16] T. Noiri, On semi continuous mappings, Atti. Accad. Naz. Lin. El. Sci. Fis. mat. Natur. 8(54)(1973), 210-214.

[17] A. P. Robertson, W.J. Robertson, Topological vector spaces. Cambridge Tracts in Mathematics. 53. Cam-bridge University Press, (1964).

[18] J. V. Wehausen, Transformations in Linear Topological Spaces, Duke Mathematical Journal, Vol. 4 (1938), 157-169.