Title

THE GENERALIZED PRE-OPEN COMPACT TOPOLOGY
ON FUNCTION SPACES

Authors

S. Mishra, S.M. Kang, M. Kumar
Department of Mathematics
Lovely Professional University
Phagwara, Punjab, 144411, INDIA
Department of Mathematics and RINS
Gyeongsang National University
Jinju, 52828, KOREA

Abstract

The aim of this paper is to introduce new topology called generalized pre-open compact topology on the set of all real-valued continuous function on a Tychonoff space and compare this topology with other well-known topologies. Furthermore, we investigated relations of this topology with the induced mapping, as well as properties like metrizibility, submetrizibility and separability.

History

Received: April 10, 2016
Revised: February 2, 2017
Published: April 21, 2017

AMS Classification, Key Words

AMS Subject Classification: 54C10, 54C35, 54D65, 54E18, 54E35
Key Words and Phrases: -compact topology, induced mapping, metrizibility, submetrizibility and separability

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1

T. Al-Hawary, Generalized preopen sets, Questions Answers, Gen. Topology, 29 (2011), 73-80.

2

T. Al-Hawary, On generalized preopen sets, Proyecciones 32 (2013), 47-60, doi: https://doi.org/10.4067/S0716-09172013000100004.

3

R. Arens, A topology for spaces of transformations, Ann. of Math., 47 (1946), 480-495, doi: https://doi.org/10.2307/1969087.

4

R. Arens, J. Dugundji, Topologies for function spaces, Pacific J. Math., 1 (1951), 5-31.

5

R.H. Fox, On topologies for function spaces, Bull. Amer. Math Soc., 51 (1945), 429-432, doi: https://doi.org/10.1090/S0002-9904-1945-08370-0.

6

P. Garg, S. Kundu, The compact--open topology on , Topology Appl., 159 (2012), 2082-2089, doi: https://doi.org/10.1016/j.topol.2012.01.017.

7

D. Gulick, The -compact-open topology and its relatives, Math. Scand., 30 (1972), 159-176, doi: https://doi.org/10.7146/math.scand.a-11072.

8

J.R. Jackson, Comparison of topologies on function spaces, Proc. Amer. Math. Soc., 3 (1952), 156-158, doi: https://doi.org/10.1090/S0002-9939-1952-0046031-5.

9

S. Kundu, Spaces of continuous linear functional: something old and something new, Topology Proc., 14 (1989), 113-129.

10

S. Kundu, The metrizability and completeness of the support-open topology on , Topology Appl., 157 (2010), 1119-1126, doi: https://doi.org/10.1016/j.topol.2010.01.002.

11

S. Kundu, P. Garg, The pseudocompact-open topology on , Topology Proc., 30 (2006), 279-299.

12

S. Kundu, P. Garg, Countability properties of the pseudocompact-open topology on : a comparative study, Rend. Istit. Mat. Univ. Trieste, 39 (2007), 421-444.

13

S. Kundu, P. Garg, The compact-open topology: a new perspective, Topology Appl., 156 (2009), 686-696, doi: https://doi.org/10.1016/j.topol.2008.09.006.

14

S. Kundu, R.A. McCoy, Topologies between compact and uniform convergence on function spaces, Internat. J. Math. Math. Sci., 16 (1993), 101-110, doi: https://doi.org/10.1155/S0161171293000122.

15

S. Kundu, A.B. Raha, The bounded-open topology and its relatives, Rend. Istit. Mat. Univ. Trieste, 27 (1995), 61-77.

16

N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 2 (1970), 89-96, doi: https://doi.org/10.1007/BF02843888.

17

R.A. McCoy, I. Ntantu, Topological Properties of Spaces of Continuous Functions, Lecture notes in mathematics, 1315, Springer-Verlag, Berlin, 1988.

18

A.V. Osipov, The -compact-open topology on function spaces, Topology Appl., 159 (2012), 3059-3066, doi: https://doi.org/10.1016/j.topol.2012.05.018.

How to Cite?

DOI: 10.12732/ijpam.v114i1.1 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 114
Issue: 1
Pages: 1 - 15

Google Scholar; DOI (International DOI Foundation); WorldCAT.

This work is licensed under the Creative Commons Attribution International License (CC BY).

---