More Properties of Semi-Linear Uniform Spaces
Author(s)
S. A. Alhihi
ABSTRACT
In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.
In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.
KEYWORDS
Lipschitz Condition, Contractions, Not Metrizable Spaces, Semi-Linear Spaces, Uniform Spaces, Fixed Point
Lipschitz Condition, Contractions, Not Metrizable Spaces, Semi-Linear Spaces, Uniform Spaces, Fixed Point
Cite this paper
Alhihi, S. (2015) More Properties of Semi-Linear Uniform Spaces. Applied Mathematics, 6, 1069-1075. doi: 10.4236/am.2015.66097.
Alhihi, S. (2015) More Properties of Semi-Linear Uniform Spaces. Applied Mathematics, 6, 1069-1075. doi: 10.4236/am.2015.66097.
References
[1] Tallafha, A. (2013) Open Problems in Semi-Linear Uniform Spaces. Journal of Applied Functional Analysis, 8, 223-228. [2] Weil, A. (1936) Les recouvrements des espaces topologiques: Espaces complete, espaces bicompact. Comptes Rendus de l’Académie des Sciences, 202, 1002-1005. [3] Weil, A. (1937) Sur les espaces a structure uniforme et sur la topologie generale. Actuarial Science India, 551, Paris. [4] Weil, A. (1938) Sur les espaces à structure uniforme et sur la topologic générale. Hermann, Paris. [5] Cohen, L.W. (1937) Uniformity Properties in a Topological Space Satisfying the First Denumerability Postulate. Duke Mathematical Journal, 3, 610-615. [6] Cohen, L.W. (1939) On Imbedding a Space in a Complete Space. Duke Mathematical Journal, 5, 174-183. [7] Graves, L.M. (1937) On the Completing of a Housdroff Space. Annals of Mathematics, 38, 61-64. [8] Bourbaki, N. (1940) Topologie Générale (General Topology). Paris. [9] James, I.M. (1987) Topological and Uniform Spaces. Undergraduate Texts in Mathematics. Springer-Verlag, Berlin. [10] Tallafha, A. and Khalil, R. (2009) Best Approximation in Uniformity Type Spaces. European Journal of Pure and Applied Mathematics, 2, 231-238. [11] Tallafha, A. (2011) Some Properties of Semi-Linear Uniform Spaces. Boletin da Sociedade Paranaense de Matematica, 29, 9-14. [12] Tallafha, A. (2015) Fixed Point in a Non-Metrizable Spaces. To Appear. [13] Engelking, R. (1968) Outline of General Topology. North-Holand, Amsterdam.
[1] Tallafha, A. (2013) Open Problems in Semi-Linear Uniform Spaces. Journal of Applied Functional Analysis, 8, 223-228. [2] Weil, A. (1936) Les recouvrements des espaces topologiques: Espaces complete, espaces bicompact. Comptes Rendus de l’Académie des Sciences, 202, 1002-1005. [3] Weil, A. (1937) Sur les espaces a structure uniforme et sur la topologie generale. Actuarial Science India, 551, Paris. [4] Weil, A. (1938) Sur les espaces à structure uniforme et sur la topologic générale. Hermann, Paris. [5] Cohen, L.W. (1937) Uniformity Properties in a Topological Space Satisfying the First Denumerability Postulate. Duke Mathematical Journal, 3, 610-615. [6] Cohen, L.W. (1939) On Imbedding a Space in a Complete Space. Duke Mathematical Journal, 5, 174-183. [7] Graves, L.M. (1937) On the Completing of a Housdroff Space. Annals of Mathematics, 38, 61-64. [8] Bourbaki, N. (1940) Topologie Générale (General Topology). Paris. [9] James, I.M. (1987) Topological and Uniform Spaces. Undergraduate Texts in Mathematics. Springer-Verlag, Berlin. [10] Tallafha, A. and Khalil, R. (2009) Best Approximation in Uniformity Type Spaces. European Journal of Pure and Applied Mathematics, 2, 231-238. [11] Tallafha, A. (2011) Some Properties of Semi-Linear Uniform Spaces. Boletin da Sociedade Paranaense de Matematica, 29, 9-14. [12] Tallafha, A. (2015) Fixed Point in a Non-Metrizable Spaces. To Appear. [13] Engelking, R. (1968) Outline of General Topology. North-Holand, Amsterdam.