| Title:
|
On weak forms of preopen and preclosed functions (English) |
| Author:
|
Caldas, Miguel |
| Author:
|
Navalagi, Govindappa |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
119-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces. (English) |
| Keyword:
|
preopen sets preclosed sets |
| Keyword:
|
weakly preclosed functions |
| Keyword:
|
extremally disconnected spaces |
| Keyword:
|
quasi H-closed spaces |
| MSC:
|
54A40 |
| MSC:
|
54C08 |
| MSC:
|
54C10 |
| MSC:
|
54D10 |
| idZBL:
|
Zbl 1111.54011 |
| idMR:
|
MR2068686 |
| . |
| Date available:
|
2008-06-06T22:43:13Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107896 |
| . |
| Reference:
|
[1] Abd-El-Monsef M. E., El-Deeb S. N., Mahmoud R. A.: $\beta $-open and $\beta $-continuous mappings.Bull. Fac. Sci. Assiut Univ. 12 (1983), 70–90. |
| Reference:
|
[2] Andrijevic D.: Semipreopen sets.Mat. Vesnik 38 (1986), 24–32. MR 0854426 |
| Reference:
|
[3] Arya S. P., Gupta R.: Strongly continuous mappings.Kyungpook Math. J. 14 (1974), 131–143. Zbl 0328.54006, MR 0407795 |
| Reference:
|
[4] Baker C. W.: Contra-open functions and contra-closed functions.Math. Today (Ahmedabad) 15 (1997), 19–24. Zbl 0903.54008, MR 1479585 |
| Reference:
|
[5] Baker C. W.: Decomposition of openness.Int. J. Math. Math. Sci. 17 (1994), 413–415. Zbl 0798.54018, MR 1261091 |
| Reference:
|
[6] Caldas M.: Weak and strong forms of irresolute maps.Int. J. Math. Math. Sci. 23 (2000), 253–259. Zbl 0982.54018, MR 1757805 |
| Reference:
|
[7] Cameron D. E.: Properties of s-closed spaces.Proc. Amer. Math. Soc. 72 (1978), 581–586. Zbl 0408.54018, MR 0514999 |
| Reference:
|
[8] Cameron D. E.: Some maximal topologies which are Q.H.C..Proc. Amer. Math. Soc. 75 (1979), 149–156. MR 0529232 |
| Reference:
|
[9] Chew J., Tong J.: Some remarks on weak continuity.Amer. Math. Monthly 98 (1991), 931–934. Zbl 0764.54007, MR 1137541 |
| Reference:
|
[10] Costovici, Gh.: Other elementary properties of the mappings of topological spaces.Bul. Inst. Politehn. Iasi. Sect. I. 26 (1980), 19–21. Zbl 0479.54006, MR 0640953 |
| Reference:
|
[11] Corson H., Michael E.: Metrizability of certain countable union.Illinois J. Math. 18 (1964), 351–360. MR 0170324 |
| Reference:
|
[12] El-Deeb S. N., Hasanein I. A., Mashhour A. S., Noiri T.: On $p$-regular spaces.Bull. Math. Soc. Sci. Math. R.S. Roum. 27 (1983), 311–315. Zbl 0524.54016, MR 0744738 |
| Reference:
|
[13] Husain T.: Almost continuous mappings.Pr. Mat. 10 (1966), 1–7. Zbl 0138.17601, MR 0220256 |
| Reference:
|
[14] Kar A., Bhattacharya P.: Weakly semicontinuous functions.J. Indian Acad. Math. 8 (1986), 83–93. MR 0914674 |
| Reference:
|
[15] Kar A., Bhattacharya P.: Some weak separation axioms.Bull. Calcutta Math. Soc. 82 (1996), 415–422. MR 1134225 |
| Reference:
|
[16] Levine N.: Strong continuity in topological spaces.Amer. Math. Monthly 67 (1960), 269. Zbl 0156.43305 |
| Reference:
|
[17] Long P. E., Carnahan D. A.: Comparing almost continuous functions.Proc. Amer. Math. Soc. 38 (1973), 413–418. Zbl 0261.54007, MR 0310824 |
| Reference:
|
[18] Maheshwari, S,. N., Prasad R.: Some new separation axioms.Ann. Soc. Sci. Bruxelles 89 (1975), 395–402. Zbl 0318.54030, MR 0385801 |
| Reference:
|
[19] Mashhour A. S., Abd El-Monsef M. E., El-Deeb S. N.: Precontinuous and weak precontinuous mappings.Proc. Math. Phys. Soc. Egypt. 53 (1982), 47–53. MR 0830896 |
| Reference:
|
[20] Mashhour A. S., Hasanein I. A., EL-Deeb S. N.: $\alpha $-continuous and $\alpha $-open mappings.Acta Math. Hungar. 41 (1983), 213–218. Zbl 0534.54006, MR 0703734 |
| Reference:
|
[21] Njastad O.: On some classes of nearly open sets.Pacific J. Math. 15 (1965), 961–970. Zbl 0137.41903, MR 0195040 |
| Reference:
|
[22] Noiri T.: A generalization of closed mappings.Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 54 (1973), 412–415. MR 0358672 |
| Reference:
|
[23] Noiri T.: On $\theta $-semicontinuous functions.Indian J. Pure Appl. Math. 21 (1990), 410–415. MR 1056351 |
| Reference:
|
[24] Ptak V.: Completeness and open mappings theorem.Bull. Soc. Math. France 86 (1958), 41–74. MR 0105606 |
| Reference:
|
[25] Popa V.: Properties of $H$-almost continuous functions.Bull. Math. Soc. Sci. Math. R.S. Roum. 31 (1987), 163–168. Zbl 0618.54013, MR 0919867 |
| Reference:
|
[26] Rose D. A.: On weak openness and almost openness.Int. J. Math. Math. Sci. 7 (1984), 35–40. MR 0743822 |
| Reference:
|
[27] Rose D. A., Jankovic D. S.: Weakly closed functions and Hausdorff spaces.Math. Nachr. 130 (1987), 105–110. Zbl 0622.54008, MR 0885619 |
| Reference:
|
[28] Singal M. K., Singal A. R.: Almost continuous mappings.Yokohama Math. J. 16 (1968), 63–73. Zbl 0191.20802, MR 0261569 |
| Reference:
|
[29] Velicko N. V.: $H$-closed topological spaces.Amer. Math. Soc. Transl. 78 (1968), 103–118. |
| Reference:
|
[30] Willard S.: General topology.Addition Wesley Publishing Company (1970). Zbl 0205.26601, MR 0264581 |
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