# On $\theta $-closed sets and some forms of continuity

Archivum Mathematicum (2004)

- Volume: 040, Issue: 4, page 383-393
- ISSN: 0044-8753

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topSaleh, Mohammad. "On $\theta $-closed sets and some forms of continuity." Archivum Mathematicum 040.4 (2004): 383-393. <http://eudml.org/doc/249287>.

@article{Saleh2004,

abstract = {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 $X$.},

author = {Saleh, Mohammad},

journal = {Archivum Mathematicum},

keywords = {almost closure continuity; $\theta $-open; $\theta $-closed; quasi-H-closed; S-Hausdorff spaces; n-compactness; almost closure continuity},

language = {eng},

number = {4},

pages = {383-393},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On $\theta $-closed sets and some forms of continuity},

url = {http://eudml.org/doc/249287},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Saleh, Mohammad

TI - On $\theta $-closed sets and some forms of continuity

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 4

SP - 383

EP - 393

AB - 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 $X$.

LA - eng

KW - almost closure continuity; $\theta $-open; $\theta $-closed; quasi-H-closed; S-Hausdorff spaces; n-compactness; almost closure continuity

UR - http://eudml.org/doc/249287

ER -

## References

top- Alexandroff P., Urysohn P., Memoire sur les espaces topologiques compacts, Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect. I 14 (1929), 1–96. (1929)
- Andrew D. R., Whittlesy E. K., Closure continuity, Amer. Math. Monthly 73 (1966), 758–759. (1966) Zbl0145.19404MR1533910
- Chew J., Tong J., Some remarks on weak continuity, Amer. Math. Monthly 98 (1991), 931–934. (1991) Zbl0764.54007MR1137541
- Fomin S., Extensions of topological spaces, C. R. Dokl. Akad. Sci. URSS (M.S.) 32 (1941), 114–116. (1941) MR0005324
- Levine N., A Decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44–46. (1961) Zbl0100.18601MR0126252
- Long P. E., Carnahan D. A., Comparing almost continuous functions, Proc. Amer. Math. Soc. 38 (1973), 413–418. (1973) Zbl0261.54007MR0310824
- Long P. E., Herrington L., Strongly $\theta $-continuous functions, J. Korean. Math. Soc. 18 (1981), 21–28. (1981) Zbl0478.54006MR0635376
- Long P. E., Herrington L., The T${}_{\theta}$-topology and faintly continuous functions, Kyungpook Math. J. 22 (1982), 7–14. (1982) Zbl0486.54009MR0672078
- Mukherjee M. N., Raychaudhuri S., Some applications of $\theta $-closure operators, Indian J. Pure Appl. Math. 26 (1995), 433–439. (1995) Zbl0846.54015MR1333081
- Noiri T., On weakly continuous mappings, Proc. Amer. Math. Soc. 46(1) (1974), 120–124. (1974) Zbl0294.54013MR0348698
- Noiri T., On $\delta $-continuous functions, J. Korean. Math. Soc. 18 (1980), 161–166. (1980) Zbl0435.54010MR0577894
- Noiri T., Popa V., Weak forms of faint continuity, Bull. Math. Soc. Sci. Math. Rouman. 34(82) (1990), 263–270. (1990) Zbl0739.54003MR1087163
- Noiri T., Properties of $\theta $-continuous functions, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), 887–891. (1975) Zbl0335.54012MR0440491
- Saleemi B., Shahzad N., Alghamdi M., Almost continuity vs closure continuity, Arch. Math. (Brno) 37 (2001), 39–44. Zbl1090.54503MR1822764
- Saleh M., Some remarks on closure and strong continuity, An Najah Univ. J. Res. 12 (1998), 7–20. (1998)
- Saleh M., Some applications of $\delta $-sets to H-closed spaces, Q&A Topology 17 (1999), 203–211. (1999) Zbl0945.54018MR1716397
- Saleh M., On almost strong $\theta $-continuity, FJMS 2000, 257-267. Zbl0982.54015MR1771247
- Saleh M., On super and $\delta $-continuities, Mathematics and Mathematics Education, World Scientific, 2002, 281–291. Zbl1010.54013MR1911242
- Saleh M., On faint and quasi-$\theta $-continuity, FJMS 11 (2003), 177–186. MR2020500
- Saleh M., On $\theta $-continuity and strong $\theta $-continuity, Applied Mathematics E-Notes (2003), 42–48. Zbl1024.54011MR1980564
- Singal M. K., Singal A. R., Almost continuous mappings, Yokohama Math. J. 16 (1968), 63–73. (1968) Zbl0191.20802MR0261569
- Veličko N. V., H-closed topological spaces, Trans. Amer. Math. Soc. 78 (1968), 103–118. (1968)

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