# Article

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Keywords:
almost closure continuity; $\theta$-open; $\theta$-closed; quasi-H-closed; S-Hausdorff spaces; n-compactness.
Summary:
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 $X$.
References:
[1] Alexandroff P., Urysohn P.: Memoire sur les espaces topologiques compacts. Verh. Nederl. Akad. Wetensch. Afd. Natuurk. Sect. I 14 (1929), 1–96.
[2] Andrew D. R., Whittlesy E. K.: Closure continuity. Amer. Math. Monthly 73 (1966), 758–759. MR 1533910 | Zbl 0145.19404
[3] Chew J., Tong J.: Some remarks on weak continuity. Amer. Math. Monthly 98 (1991), 931–934. MR 1137541 | Zbl 0764.54007
[4] Fomin S.: Extensions of topological spaces. C. R. Dokl. Akad. Sci. URSS (M.S.) 32 (1941), 114–116. MR 0005324
[5] Levine N.: A Decomposition of continuity in topological spaces. Amer. Math. Monthly 68 (1961), 44–46. MR 0126252 | Zbl 0100.18601
[6] Long P. E., Carnahan D. A.: Comparing almost continuous functions. Proc. Amer. Math. Soc. 38 (1973), 413–418. MR 0310824 | Zbl 0261.54007
[7] Long P. E., Herrington L.: Strongly $\theta$-continuous functions. J. Korean. Math. Soc. 18 (1981), 21–28. MR 0635376 | Zbl 0478.54006
[8] Long P. E., Herrington L.: The T$_{\theta }$-topology and faintly continuous functions. Kyungpook Math. J. 22 (1982), 7–14. MR 0672078 | Zbl 0486.54009
[9] Mukherjee M. N., Raychaudhuri S.: Some applications of $\theta$-closure operators. Indian J. Pure Appl. Math. 26 (1995), 433–439. MR 1333081 | Zbl 0846.54015
[10] Noiri T.: On weakly continuous mappings. Proc. Amer. Math. Soc. 46(1) (1974), 120–124. MR 0348698 | Zbl 0294.54013
[11] Noiri T.: On $\delta$-continuous functions. J. Korean. Math. Soc. 18 (1980), 161–166. MR 0577894 | Zbl 0435.54010
[12] Noiri T., Popa V.: Weak forms of faint continuity. Bull. Math. Soc. Sci. Math. Rouman. 34(82) (1990), 263–270. MR 1087163 | Zbl 0739.54003
[13] Noiri T.: Properties of $\theta$-continuous functions. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), 887–891. MR 0440491 | Zbl 0335.54012
[14] Saleemi B., Shahzad N., Alghamdi M.: Almost continuity vs closure continuity. Arch. Math. (Brno) 37 (2001), 39–44. MR 1822764 | Zbl 1090.54503
[15] Saleh M.: Some remarks on closure and strong continuity. An Najah Univ. J. Res. 12 (1998), 7–20.
[16] Saleh M.: Some applications of $\delta$-sets to H-closed spaces. Q&A Topology 17 (1999), 203–211. MR 1716397 | Zbl 0945.54018
[17] Saleh M.: On almost strong $\theta$-continuity. FJMS 2000, 257-267. MR 1771247 | Zbl 0982.54015
[18] Saleh M.: On super and $\delta$-continuities. Mathematics and Mathematics Education, World Scientific, 2002, 281–291. MR 1911242 | Zbl 1010.54013
[19] Saleh M.: On faint and quasi-$\theta$-continuity. FJMS 11 (2003), 177–186. MR 2020500
[20] Saleh M.: On $\theta$-continuity and strong $\theta$-continuity. Applied Mathematics E-Notes (2003), 42–48. MR 1980564 | Zbl 1024.54011
[21] Singal M. K., Singal A. R.: Almost continuous mappings. Yokohama Math. J. 16 (1968), 63–73. MR 0261569 | Zbl 0191.20802
[22] Veličko N. V.: H-closed topological spaces. Trans. Amer. Math. Soc. 78 (1968), 103–118.

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