Geodesic
A note on weakly $(\mu ,\lambda )$-closed functions
Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 397-405

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In this paper we introduce a new class of functions called weakly $(\mu ,\lambda )$-closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly $(\mu ,\lambda )$-closed functions enable us to facilitate the formulation of certain unified theories for different weaker forms of closed functions.
In this paper we introduce a new class of functions called weakly $(\mu ,\lambda )$-closed functions with the help of generalized topology which was introduced by Á. Császár. Several characterizations and some basic properties of such functions are obtained. The connections between these functions and some other similar types of functions are given. Finally some comparisons between different weakly closed functions are discussed. This weakly $(\mu ,\lambda )$-closed functions enable us to facilitate the formulation of certain unified theories for different weaker forms of closed functions.
DOI : 10.21136/MB.2013.143512
Classification : 54A05, 54C10
Keywords: $\mu $-open set; weakly $(\mu, \lambda )$-closed function; contra $(\mu, \lambda )$-open function; strongly $(\mu, \lambda )$-continuous function 
Roy, Bishwambhar. A note on weakly $(\mu ,\lambda )$-closed functions. Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 397-405. doi: 10.21136/MB.2013.143512
@article{10_21136_MB_2013_143512,
     author = {Roy, Bishwambhar},
     title = {A note on weakly $(\mu ,\lambda )$-closed functions},
     journal = {Mathematica Bohemica},
     pages = {397--405},
     year = {2013},
     volume = {138},
     number = {4},
     doi = {10.21136/MB.2013.143512},
     mrnumber = {3231094},
     zbl = {06260040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143512/}
}
TY  - JOUR
AU  - Roy, Bishwambhar
TI  - A note on weakly $(\mu ,\lambda )$-closed functions
JO  - Mathematica Bohemica
PY  - 2013
SP  - 397
EP  - 405
VL  - 138
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143512/
DO  - 10.21136/MB.2013.143512
LA  - en
ID  - 10_21136_MB_2013_143512
ER  - 
%0 Journal Article
%A Roy, Bishwambhar
%T A note on weakly $(\mu ,\lambda )$-closed functions
%J Mathematica Bohemica
%D 2013
%P 397-405
%V 138
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143512/
%R 10.21136/MB.2013.143512
%G en
%F 10_21136_MB_2013_143512

[1] Caldas, M., Ekici, E., Jafari, S., Moshoka, S. P.: On weak $BR$-closed functions between topological spaces. Math. Commun. 14 (2009), 67-73. | MR

[2] Császár, Á.: Generalized topology, generalized continuity. Acta Math. Hung. 96 (2002), 351-357. | DOI | MR | Zbl

[3] Császár, Á.: Generalized open sets in generalized topologies. Acta Math. Hung. 106 (2005), 53-66. | DOI | MR | Zbl

[4] Császár, Á.: Normal generalized topologies. Acta Math. Hung. 115 (2007), 309-313. | DOI | MR | Zbl

[5] Császár, Á.: $\delta$- and $\theta$-modifications of generalized topologies. Acta Math. Hung. 120 (2008), 275-279. | DOI | MR | Zbl

[6] Császár, Á.: Remarks on quasi-topologies. Acta Math. Hung. 119 (2008), 197-200. | DOI | MR | Zbl

[7] Ekici, E.: Generalized hyperconnectedness. Acta Math. Hung. 133 (2011), 140-147. | DOI | MR | Zbl

[8] Ekici, E.: Generalization of weakly clopen and strongly $\theta$-$b$-continuous functions. Chaos Solitons Fractals 38 (2008), 79-88. | DOI | MR | Zbl

[9] Ergun, N., Noiri, T.: On weakly closed functions. Mat. Vesn. 42 (1990), 167-176. | MR | Zbl

[10] Min, W. K.: A note on $\theta(g,g')$-continuity in generalized topological spaces. Acta Math. Hung. 125 (2009), 387-393. | DOI | MR | Zbl

[11] Njåstad, O.: On some classes of nearly open sets. Pac. J. Math. 15 (1965), 961-970. | DOI | MR | Zbl

[12] Noiri, T.: A generalization of closed mappings. Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 54(1973) (1974), 412-415. | MR | Zbl

[13] Rose, D. A., Janković, D. S.: Weakly closed functions and Hausdorff spaces. Math. Nachr. 130 (1987), 105-110. | DOI | MR | Zbl

[14] Roy, B.: On a type of generalized open sets. Appl. Gen. Topol. 12 (2011), 163-173. | MR | Zbl

[15] Stone, M. H.: Application of the theory of Boolean rings to general Topology. Trans. Am. Math. Soc. 41 (1937), 375-481. | DOI | MR

Cité par Sources :