Title:
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On $\theta $-closed sets and some forms of continuity (English) |
Author:
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Saleh, Mohammad |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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40 |
Issue:
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4 |
Year:
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2004 |
Pages:
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383-393 |
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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In this paper, we further the study of $\theta $-compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using $\theta $-open and $\delta $-open sets. Among other results, it is shown a weakly $\theta $-retract of a Hausdorff space $X$ is a $\delta $-closed subset of $X$. (English) |
Keyword:
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almost closure continuity |
Keyword:
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$\theta $-open |
Keyword:
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$\theta $-closed |
Keyword:
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quasi-H-closed |
Keyword:
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S-Hausdorff spaces |
Keyword:
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n-compactness. |
MSC:
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54C08 |
MSC:
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54D05 |
MSC:
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54D30 |
idZBL:
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Zbl 1111.54014 |
idMR:
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MR2129960 |
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Date available:
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2008-06-06T22:44:29Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107922 |
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Reference:
|
[1] Alexandroff P., Urysohn P.: Memoire sur les espaces topologiques compacts.Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect. I 14 (1929), 1–96. |
Reference:
|
[2] Andrew D. R., Whittlesy E. K.: Closure continuity.Amer. Math. Monthly 73 (1966), 758–759. Zbl 0145.19404, MR 1533910 |
Reference:
|
[3] Chew J., Tong J.: Some remarks on weak continuity.Amer. Math. Monthly 98 (1991), 931–934. Zbl 0764.54007, MR 1137541 |
Reference:
|
[4] Fomin S.: Extensions of topological spaces.C. R. Dokl. Akad. Sci. URSS (M.S.) 32 (1941), 114–116. MR 0005324 |
Reference:
|
[5] Levine N.: A Decomposition of continuity in topological spaces.Amer. Math. Monthly 68 (1961), 44–46. Zbl 0100.18601, MR 0126252 |
Reference:
|
[6] Long P. E., Carnahan D. A.: Comparing almost continuous functions.Proc. Amer. Math. Soc. 38 (1973), 413–418. Zbl 0261.54007, MR 0310824 |
Reference:
|
[7] Long P. E., Herrington L.: Strongly $\theta $-continuous functions.J. Korean. Math. Soc. 18 (1981), 21–28. Zbl 0478.54006, MR 0635376 |
Reference:
|
[8] Long P. E., Herrington L.: The T$_{\theta }$-topology and faintly continuous functions.Kyungpook Math. J. 22 (1982), 7–14. Zbl 0486.54009, MR 0672078 |
Reference:
|
[9] Mukherjee M. N., Raychaudhuri S.: Some applications of $ \theta $-closure operators.Indian J. Pure Appl. Math. 26 (1995), 433–439. Zbl 0846.54015, MR 1333081 |
Reference:
|
[10] Noiri T.: On weakly continuous mappings.Proc. Amer. Math. Soc. 46(1) (1974), 120–124. Zbl 0294.54013, MR 0348698 |
Reference:
|
[11] Noiri T.: On $\delta $-continuous functions.J. Korean. Math. Soc. 18 (1980), 161–166. Zbl 0435.54010, MR 0577894 |
Reference:
|
[12] Noiri T., Popa V.: Weak forms of faint continuity.Bull. Math. Soc. Sci. Math. Rouman. 34(82) (1990), 263–270. Zbl 0739.54003, MR 1087163 |
Reference:
|
[13] Noiri T.: Properties of $\theta $-continuous functions.Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), 887–891. Zbl 0335.54012, MR 0440491 |
Reference:
|
[14] Saleemi B., Shahzad N., Alghamdi M.: Almost continuity vs closure continuity.Arch. Math. (Brno) 37 (2001), 39–44. Zbl 1090.54503, MR 1822764 |
Reference:
|
[15] Saleh M.: Some remarks on closure and strong continuity.An Najah Univ. J. Res. 12 (1998), 7–20. |
Reference:
|
[16] Saleh M.: Some applications of $\delta $-sets to H-closed spaces.Q&A Topology 17 (1999), 203–211. Zbl 0945.54018, MR 1716397 |
Reference:
|
[17] Saleh M.: On almost strong $\theta $-continuity.FJMS 2000, 257-267. Zbl 0982.54015, MR 1771247 |
Reference:
|
[18] Saleh M.: On super and $\delta $-continuities.Mathematics and Mathematics Education, World Scientific, 2002, 281–291. Zbl 1010.54013, MR 1911242 |
Reference:
|
[19] Saleh M.: On faint and quasi-$\theta $-continuity.FJMS 11 (2003), 177–186. MR 2020500 |
Reference:
|
[20] Saleh M.: On $\theta $-continuity and strong $\theta $-continuity.Applied Mathematics E-Notes (2003), 42–48. Zbl 1024.54011, MR 1980564 |
Reference:
|
[21] Singal M. K., Singal A. R.: Almost continuous mappings.Yokohama Math. J. 16 (1968), 63–73. Zbl 0191.20802, MR 0261569 |
Reference:
|
[22] Veličko N. V.: H-closed topological spaces.Trans. Amer. Math. Soc. 78 (1968), 103–118. |
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