s-Topological vector spaces
محورهای موضوعی : General topologyM. Khan 1 , S. Azam 2 , S. Bosan 3
1 - Department of Mathematics, COMSATS Institute of Information
Technology, Park Road, Islamabad, Pakistan
2 - Punjab Education Department, Pakistan
3 - Punjab Education Department, Pakistan
کلید واژه: s-Topological vector space, Semi-open set, semi-closed set, s-continuous mapping, left (right) translation, generalized homeomorphism, generalized homogeneous space, semi-continuous mapping,
چکیده مقاله :
In this paper, we have defined and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are defined by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. Every open subspaceof an s-topological vector space is an s-topological vector space. A homomorphism betweens-topological vector spaces is semi-continuous if it is s-continuous at the identity.
[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] Kolmogroff, 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.
