Isaac Scientific Publishing

Advances in Analysis

Topological Properties of Distance Space

Download PDF (511.7 KB) PP. 8 - 17 Pub. Date: July 8, 2016

DOI: 10.22606/aan.2016.11002

Author(s)

  • P Sumati Kumari*
    Department of Mathematics, National Institute of Technology-A.P, Tadepalligudem, A.P, India.
  • I.Ramabhadra Sarma
    Department of Mathematics, Acharya Nagarjuna University, A.P, India.
  • J.Madhusudana Rao
    Department of Mathematics, Vijaya College of Engineering, Khammam, Telangana, India.

Abstract

In this paper, we intended to explain through some examples the usefulness and necessity of studying the topological properties of weaker forms of distance spaces.

Keywords

Distance space, continuity.

References

[1] Frechet C F, Surquelques points du calcul fonctionnal, Rendiconti del Circolo Mathematico di Palermo,vol.22.(2nd semester, 1-74,1906).

[2] Chittenden E W, On the equivalence of ecart and voisinage,Trans. Amer.Math. Soc. Vol.18, 161?£?166, 1917.

[3] Fisher B, Mappings on metric spaces, Acta.Math.Acad.Hung, Vol.32, 283- 285, 1978.

[4] Cf. A. H. Frink, ’Distance functions and the metrization problem’. Bull.Amer. Math. Soc. , Vol.43,1937.

[5] Wilson W A, On Semi Metric Spaces, American Journal of Mathematics, Vol.53,No.2, 361-373, 1931.

[6] P Hitzler, Generalized metrics and topology in logic programming semantics, Ph. D Thesis, National University of Ireland (University College, Cork), 2001.

[7] Hausdorff Felix, Grundz?ge der Mengenlehre, Veit and Company, Leipzig, 1914.

[8] Jozef Dobos , Metric Preserving Functions, Stroffek,1998.

[9] I R Sarma, P Sumati Kumari,On Dislocated Metric spaces, International Journal of Mathematical Archive, vol. 3, No. 1, 1-6 2012.

[10] P Sumati Kumari, On Dislocated Quasi Metrics, Journal of Advanced Studies in Topology, Vol. 3, No. 2, 66 -74,2012.

[11] Kumari, PS, Ramana, CV, Zoto, K: On quasi-symmetric space. Indian J. Sci. Technol. 7(10), 1583-1587 (2014).

[12] Abbas, et al.: Generalized coupled common fixed point results in partially ordered A-metric spaces. Fixed Point Theory Appl. 2015, Article ID 64 (2015)

[13] Kumari, PS, Panthi, D: Cyclic contractions and fixed point theorems on various generating spaces. Fixed Point Theory Appl. 2015, Article ID 153 (2015).

[14] Kumari, P. Sumati, and Muhammad Sarwar, Some fixed point theorems in generating space of b-quasi-metric family, SpringerPlus 5.1 (2016): 1.