Title:
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Mildly ($1,2)^*$-normal spaces and some bitopological functions (English) |
Author:
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Kayathri, K. |
Author:
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Ravi, O. |
Author:
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Thivagar, M. L. |
Author:
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Israel, M. Joseph |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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135 |
Issue:
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1 |
Year:
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2010 |
Pages:
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1-13 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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The aim of the paper is to introduce and study a new class of spaces called mildly $(1,2)^*$-normal spaces and a new class of functions called $(1,2)^*$-$\mathop{\rm rg}$-continuous, $(1,2)^*$-${\rm R}$-map, almost $(1,2)^*$-continuous function and almost $(1,2)^*$-${\rm rg}$-closed function in bitopological spaces. Subsequently, the relationships between mildly $(1,2)^*$-normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly $(1,2)^*$-normal spaces, properties of the new bitopological functions and preservation theorems for mildly $(1,2)^*$-normal spaces in bitopological spaces. (English) |
Keyword:
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mildly $(1,2)^*$-normal space |
Keyword:
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$(1,2)^*$-${\rm rg}$-closed set |
Keyword:
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$(1,2)^*$-${\rm rg}$-continuous function |
Keyword:
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almost $(1,2)^*$-continuous function |
Keyword:
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almost $(1,2)^*$-${\rm rg}$-closed function |
MSC:
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54E55 |
idZBL:
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Zbl 1224.54069 |
idMR:
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MR2643351 |
DOI:
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10.21136/MB.2010.140676 |
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Date available:
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2010-07-20T18:18:22Z |
Last updated:
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2020-07-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140676 |
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Reference:
|
[1] Arya, S. P., Gupta, R.: On strongly continuous mappings.Kyungpook Math. J. 14 (1974), 131-143. Zbl 0328.54006, MR 0407795 |
Reference:
|
[2] Arya, S. P., Nour, T.: Characterizations of $s$-normal spaces.Indian J. Pure Appl. Math. 21 (1990), 717-719. Zbl 0706.54021, MR 1069994 |
Reference:
|
[3] Dontchev, J., Noiri, T.: Quasi-normal spaces and $\pi$g-closed sets.Acta Math. Hungar. 89 (2000), 211-219. Zbl 0973.54013, MR 1912602, 10.1023/A:1010607824929 |
Reference:
|
[4] Ekici, E.: On $\gamma$ normal spaces.Bull. Math. Soc. Sci. Math. Roumanie 50 (2007), 259-272. Zbl 1150.54023, MR 2354467 |
Reference:
|
[5] Naschie, M. S. El: On the uncertainty of Cantorian geometry and two slit experiment.Chaos, Soliton and Fractals 9 (1998), 15-31. MR 1625647 |
Reference:
|
[6] Naschie, M. S. El: Quantum gravity from descriptive set theory.Chaos, Soliton and Fractals 19 (2004), 1339-1344. Zbl 1075.83513, 10.1016/j.chaos.2003.08.009 |
Reference:
|
[7] Ganster, M., Jafari, S., Navalagi, G. B.: On semi-$g$-regular and semi-$g$-normal spaces.Demonstratio Math. 35 (2002), 415-421. Zbl 1026.54013, MR 1907314 |
Reference:
|
[8] Khalimsky, E. D.: Applications of connected ordered topological spaces in topology.Conference of Mathematics Department of Povolsia, 1970. |
Reference:
|
[9] Khalimsky, E. D., Kopperman, R., Meyer, P. R.: Computer graphics and connected topologies on finite ordered sets.Topol. Appl. 36 (1990), 1-17. Zbl 0709.54017, MR 1062180, 10.1016/0166-8641(90)90031-V |
Reference:
|
[10] Kohli, J. K., Das, A. K.: New normality axioms and decompositions of normality.Glasnik Mat. 37 (2002), 163-173. Zbl 1042.54014, MR 1918103 |
Reference:
|
[11] Kong, T. Y., Kopperman, R., Meyer, P. R.: A topological approach to digital topology.Am. Math. Month. 98 (1991), 901-917. Zbl 0761.54036, MR 1137537, 10.2307/2324147 |
Reference:
|
[12] Kovalevsky, V., Kopperman, R.: Some topology-based image processing algorithms.Ann. NY Acad Sci. 728 (1994), 174-182. Zbl 0913.68216, MR 1467772, 10.1111/j.1749-6632.1994.tb44143.x |
Reference:
|
[13] Levine, N.: Generalized closed sets in topology.Rend. Circ. Mat. Palermo 19 (1970), 89-96. Zbl 0231.54001, MR 0305341, 10.1007/BF02843888 |
Reference:
|
[14] Maheshwari, S. N., Prasad, R.: On $s$-normal spaces.Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 22 (1978), 27-29. Zbl 0373.54016, MR 0482656 |
Reference:
|
[15] Malghan, S. R.: Generalized closed maps.J. Karnataka Univ. Sci. 27 (1982), 82-88. Zbl 0578.54008, MR 0773568 |
Reference:
|
[16] Noiri, T.: A note on mildly normal spaces.Kyungpook Math. J. 13 (1973), 225-228. Zbl 0283.54011, MR 0339074 |
Reference:
|
[17] Noiri, T.: Mildly normal spaces and some functions.Kyungpook Math. J. 36 (1996), 183-190. Zbl 0873.54016, MR 1396023 |
Reference:
|
[18] Noiri, T.: Super continuity and some strong forms of continuity.Indian J. Pure Appl. Math. 15 (1984), 241-250. Zbl 0546.54016, MR 0737147 |
Reference:
|
[19] Noiri, T.: On $s$-normal spaces and pre gs-closed functions.Acta Math. Hungar. 80 (1998), 105-113. Zbl 0909.54016, MR 1624546, 10.1023/A:1006576826569 |
Reference:
|
[20] Noiri, T.: Semi-normal spaces and some functions.Acta Math. Hungar. 65 (1994), 305-311. Zbl 0858.54019, MR 1281440, 10.1007/BF01875158 |
Reference:
|
[21] Palaniappan, N., Rao, K. C.: Regular generalized closed sets.Kyungpook Math. J. 33 (1993), 211-219. Zbl 0794.54002, MR 1253673 |
Reference:
|
[22] Park, J. K., Park, J. H.: Mildly generalized closed sets, almost normal and mildly normal spaces.Chaos, Solitons and Fractals 20 (2004), 1103-1111. Zbl 1053.54502, MR 2030343, 10.1016/j.chaos.2003.09.025 |
Reference:
|
[23] Paul, Bhattacharyya: On p-normal spaces.Soochow J. Math. 21 (1995), 273-289. |
Reference:
|
[24] Ravi, O., Thivagar, M. L.: On stronger forms of $(1,2)^*$-quotient mappings in bitopological spaces.Internat. J. Math. Game Theory and Algebra 14 (2004), 481-492. Zbl 1129.54310, MR 2174909 |
Reference:
|
[25] Ravi, O., Thivagar, M. L., Jinli, Jin: Remarks on extensions of $(1,2)^*$-${\rm g}$-closed mappings in bitopological spaces (submitted).. |
Reference:
|
[26] Ravi, O., Thivagar, M. L.: Remarks on $\lambda$-irresolute functions via $(1,2)^*$-sets, (submitted).. |
Reference:
|
[27] Ravi, O., Thivagar, M. L., Ekici, E.: Decompositions of bitopological $(1,2)^*$-continuity and complete $(1,2)^*$-continuity.Analele Universitatii Din Oradea-Fascicola Mathematica 15 (2008), 29-37. Zbl 1148.54324, MR 2422468 |
Reference:
|
[28] Ravi, O., Kayathri, K., Thivagar, M. L., Israel, M. Joseph: On $(1,2)^*$-sets and weakly generalized $(1,2)^*$-continuous maps in bitopological spaces (submitted).. |
Reference:
|
[29] Singal, M. K., Arya, S. P.: On almost-regular spaces.Glasnik Mat. 4 (1969), 89-99. Zbl 0169.24902, MR 0243483 |
Reference:
|
[30] Singal, M. K., Singal, A. R.: Almost-continuous mappings.Yokohama Math. J. 16 (1968), 63-73. Zbl 0191.20802, MR 0261569 |
Reference:
|
[31] Singal, M. K., Singal, A. R.: Mildly normal spaces.Kyungpook Math. J. 13 (1973), 27-31. Zbl 0266.54006, MR 0362215 |
Reference:
|
[32] Singal, M. K., Arya, S. P.: On almost normal and almost completely regular spaces.Glasnik Mat. 5 (1970), 141-152. MR 0275354 |
Reference:
|
[33] Vigilino, G.: Semi normal and C-compact spaces.Duke J. Math. 38 (1971), 57-61. 10.1215/S0012-7094-71-03808-7 |
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