| Title:
|
A note on weakly $(\mu ,\lambda )$-closed functions (English) |
| Author:
|
Roy, Bishwambhar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
397-405 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$\mu $-open set |
| Keyword:
|
weakly $(\mu ,\lambda )$-closed function |
| Keyword:
|
contra $(\mu ,\lambda )$-open function |
| Keyword:
|
strongly $(\mu ,\lambda )$-continuous function |
| MSC:
|
54A05 |
| MSC:
|
54C10 |
| idZBL:
|
Zbl 06260040 |
| idMR:
|
MR3231094 |
| DOI:
|
10.21136/MB.2013.143512 |
| . |
| Date available:
|
2013-11-09T20:25:23Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143512 |
| . |
| Reference:
|
[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 2732586 |
| Reference:
|
[2] Császár, Á.: Generalized topology, generalized continuity.Acta Math. Hung. 96 (2002), 351-357. Zbl 1006.54003, MR 1922680, 10.1023/A:1019713018007 |
| Reference:
|
[3] Császár, Á.: Generalized open sets in generalized topologies.Acta Math. Hung. 106 (2005), 53-66. Zbl 1076.54500, MR 2127051, 10.1007/s10474-005-0005-5 |
| Reference:
|
[4] Császár, Á.: Normal generalized topologies.Acta Math. Hung. 115 (2007), 309-313. Zbl 1135.54301, MR 2327983, 10.1007/s10474-007-5249-9 |
| Reference:
|
[5] Császár, Á.: $\delta$- and $\theta$-modifications of generalized topologies.Acta Math. Hung. 120 (2008), 275-279. Zbl 1164.54003, MR 2429524, 10.1007/s10474-007-7136-9 |
| Reference:
|
[6] Császár, Á.: Remarks on quasi-topologies.Acta Math. Hung. 119 (2008), 197-200. Zbl 1164.54002, MR 2400806, 10.1007/s10474-007-7023-4 |
| Reference:
|
[7] Ekici, E.: Generalized hyperconnectedness.Acta Math. Hung. 133 (2011), 140-147. Zbl 1249.54003, MR 2827060, 10.1007/s10474-011-0086-2 |
| Reference:
|
[8] Ekici, E.: Generalization of weakly clopen and strongly $\theta$-$b$-continuous functions.Chaos Solitons Fractals 38 (2008), 79-88. Zbl 1142.54330, MR 2417645, 10.1016/j.chaos.2008.01.012 |
| Reference:
|
[9] Ergun, N., Noiri, T.: On weakly closed functions.Mat. Vesn. 42 (1990), 167-176. Zbl 0789.54016, MR 1163949 |
| Reference:
|
[10] Min, W. K.: A note on $\theta(g,g')$-continuity in generalized topological spaces.Acta Math. Hung. 125 (2009), 387-393. Zbl 1224.54039, MR 2564436, 10.1007/s10474-009-9075-0 |
| Reference:
|
[11] Njåstad, O.: On some classes of nearly open sets.Pac. J. Math. 15 (1965), 961-970. Zbl 0137.41903, MR 0195040, 10.2140/pjm.1965.15.961 |
| Reference:
|
[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. Zbl 0283.54001, MR 0358672 |
| Reference:
|
[13] Rose, D. A., Janković, D. S.: Weakly closed functions and Hausdorff spaces.Math. Nachr. 130 (1987), 105-110. Zbl 0622.54008, MR 0885619, 10.1002/mana.19871300109 |
| Reference:
|
[14] Roy, B.: On a type of generalized open sets.Appl. Gen. Topol. 12 (2011), 163-173. Zbl 1236.54019, MR 2864008 |
| Reference:
|
[15] Stone, M. H.: Application of the theory of Boolean rings to general Topology.Trans. Am. Math. Soc. 41 (1937), 375-481. MR 1501905, 10.1090/S0002-9947-1937-1501905-7 |
| . |
