IJPAM: Volume 118, No. 1 (2018)

Title

ON A TOPOLOGY BETWEEN THE TOPOLOGIES $\tau_{\theta}$ AND $\tau_{\theta\mbox{-}\mathcal{I}}$

Authors

José Sanabria$^1$, Ennis Rosas$^2$, Margot Salas$^3$,
Carlos Carpintero$^4$, Rafael Lozada$^5$
$^{1,2,3,4}$Departamento de Matemáticas
Universidad de Oriente
Cumaná, VENEZUELA
$^1$Facultad de Ciencias Básicas
Universidad del Atlántico
Barranquilla, COLOMBIA
$^2$Departamento de Ciencias Naturales y Exactas
Universidad de la Costa
Barranquilla, COLOMBIA
$^3$Departamento de Matemáticas Aplicadas y Ciencias de la Computación
Universidad del Rosario
Bogotá, COLOMBIA
$^4$Vicerrectorıa de Investigación
Universidad Autónoma del Caribe
Barranquilla, COLOMBIA
$^5$Postgrado en Matemáticas
Universidad de Oriente
Cumaná, VENEZUELA

Abstract

We introduce a new class of sets, namely $\delta\theta$-$\mathcal{I}$-open sets, which form a topology finer than the topology $\tau_{\theta}$ formed by the class of $\theta$-open sets and coarser than the topology $\tau_{\theta\mbox{-}\mathcal{I}}$ formed by the class of $\theta$-$\mathcal{I}$-open sets. Moreover, we investigated some interesting properties of this class of sets and its relationship with the classes of the $\theta$-open, $\theta$-$\mathcal{I}$-open and $\delta$-$\mathcal{I}$-open sets.

History

Received: 2017-04-25
Revised: 2017-10-06
Published: February 16, 2018

AMS Classification, Key Words

AMS Subject Classification: 54A05, 54A10
Key Words and Phrases: $\theta$-open, ideals, $\theta$-$\mathcal{I}$-open, $\delta$-local function, $\delta\theta$-$\mathcal{I}$-open

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Bibliography

1
M. Akdag, $\theta$-$\mathcal{I}$-open sets, Kochi J. Math., 3 (2008), 217-229.

2
W. Al-Omeri, M. Noorani and A. Al-Omari, $a$-local function and its properties in ideal topological space, Fasc. Math., 53 (2014), 5-15.

3
W. Al-Omeri, M. Noorani and A. Al-Omari, On topological groups via $a$-local functions, Appl. Gen. Topol., 15 (2014), 33-42, doi: https://doi.org/10.4995/agt.2014.2126.

4
J. Cao, M. Ganster, I. Reilly and M. Steiner, $\delta$-closure, $\theta$-closure and generalized closed sets, Appl. Gen. Topol., 6 (2005), 79-86, doi: https://doi.org/10.4995/agt.2005.1964.

5
E. Hatir, A. Al-Omari and S. Jafari, $\delta$-local functions and its properties in ideal topological spaces, Fasc. Math., 53 (2014), 53-64.

6
D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295-310.

7
K. Kuratowski, Topologie I, Monografie Matematyczne tom 3, PWN-Polish Scientific Publishers, Warszawa, 1933.

8
R. L. Newcomb, Topologies wich are Compact Modulo an Ideal, Ph. D. Dissertation, Univ. of Cal. at Santa Barbara, 1967.

9
D. Sivaraj, A note on extremally disconnected spaces, Indian J. Pure Appl. Math., 17 (1986), 1373-1375.

10
K. Thanalakshmi, V. Renukadevi and D. Sivaraj, On $\theta$-$\mathcal{I}$-open sets and $\star$-extremally disconnected spaces, Kochi J. Math., 7 (2012), 17-33.

11
N. V. Veličko, $H$-closed topological spaces, Amer. Math. Soc. Transl., 78 (1968), 103-118.

12
S. Yüksel, A. Açikgöz and T. Noiri, $\delta$-$\mathcal{I}$-continuous functions, Turk. J. Math., 29 (2005), 39-51.

How to Cite?

DOI: 10.12732/ijpam.v118i1.6 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: 2018
Volume: 118
Issue: 1
Pages: 65 - 76


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