A study of topological structures on equi-continuous mappings

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2021-02-0020

Keywords:

Topology, Uniform space, Function spaces, Equi-continuous mappings

Abstract

Function space topologies are developed for EC(Y,Z), the class of equi-continuous mappings from a topological space Y to a uniform space Z. Properties such as splittingness, admissibility etc. are defined for such spaces. The net theoretic investigations are carried out to provide characterizations of splittingness and admissibility of function spaces on EC(Y,Z). The open-entourage topology and pointtransitive-entourage topology are shown to be admissible and splitting respectively. Dual topologies are defined. A topology on EC(Y,Z) is found to be admissible (resp. splitting) if and only if its dual is so.

 

Downloads

Download data is not yet available.

Author Biographies

  • Ankit Gupta, University of Delhi

    Bharati College, Dept. of Mathematics.

  • Ratna Dev Sarma, University of Delhi

    Bharati College, Dept. of Mathematics.

References

R. Arens and J. Dugundji, “Topologies for function spaces”, Pacific journal of mathematics, vol. 1, no. 1, pp. 5-31, 1951, doi: 10.2140/pjm.1951.1.5

G. Beer and S. Levi, “Strong uniform continuity”, Journal of mathematics analysis and applied, vol. 350, no. 2, pp. 568-589, 2009, doi: 10.1016/j.jmaa.2008.03.058

J. Cao and A. H. Tomita, “Bornologies, topological games and function spaces”, Topology and its applications, vol. 184, pp. 16-28, 2015, doi: 10.1016/j.topol.2015.01.009

S. Dolecki and F. Mynard, “A unified theory of function spaces and hyperspaces: local properties”, Houston journal of mathematics, vol. 40, no. 1, pp. 285-318, 2014.

D. N. Georgiou, S. D. Iliadis, and B. K. Papadopoulos, “On dual topologies”, Topology and its applications, vol. 140, no. 1, pp. 57-68, 2004, doi: 10.1016/j.topol.2003.08.015

D. N. Georgiou, S. D. Iliadis, “On the greatest splitting topology”, Topology and its applications, vol. 156, no. 1, pp. 70-75, 2008, doi: 10.1016/j.topol.2007.11.008

A. Gupta and R. D. Sarma, “Function space topologies for generalized topological spaces”, Journal of advanced research in pure mathematics, vol. 7, no. 4, pp. 103-112, 2015. [On line]. Available: https://bit.ly/2OqEPdz

A. Gupta and R. D. Sarma, “A study of function space topologies for multifunctions”, Applied general topology, vol. 18, no. 2, pp. 331-344, 2017, doi: 10.4995/agt.2017.7149.

F. Jordan, “Coincidence of function space topologies”, Topology and its applications, vol. 157, no. 2, pp. 336-351, 2010, doi: 10.1016/j.topol.2009.09.002

J. K. Kohli and A. R. Prasannan, “Fuzzy topologies on function spaces”, Fuzzy sets and systems, vol. 116, no. 3, pp. 415-420, 2000, doi: 10.1016/S0165-0114(98)00383-2

J. K. Kohli and A. R. Prasannan, “Starplus-compactness and starplus-compact open fuzzy topologies on function spaces”, Journal of mathematics and analysis applications, vol. 254, no. 1, pp. 87-100, 2001, doi: 10.1006/jmaa.2000.7208

P. S. Kumari, I. R. Sarma, and J. M. Rao, “Metrization theorem for a weaker class of uniformities”, Afrika mathematics, vol. 27, pp. 667-672, 2016, doi: 10.1007/s13370-015-0369-9

S. Kundu and A. B. Raha, “The bounded-open topology and its relatives”, Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 27, no. 1-2, pp. 61-77, 1995. [On line]. Available: https://bit.ly/36X541B

S. Kundu and P. Garg, “The pseudocompact-open topology on C(X)”, Topology proceedings, vol. 30, no. 1, pp. 279-299, 2006. [On line]. Available: https://bit.ly/36Z5Evx

Downloads

Published

2021-02-16

Issue

Section

Artículos

How to Cite

[1]
“A study of topological structures on equi-continuous mappings”, Proyecciones (Antofagasta, On line), vol. 40, no. 2, pp. 335–354, Feb. 2021, doi: 10.22199/issn.0717-6279-2021-02-0020.