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Keywords:
almost continuous function; weakly continuous function
almost continuous function; weakly continuous function
Summary:
It is well known that a function $f$ from a space $X$ into a space $Y$ is continuous if and only if, for every set $K$ in $X$ the image of the closure of $K$ under $f$ is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets $K$ of $X$.
References:
[1] Dontchev J., Noiri T.: A note on Saleh’s paper “Almost continuity implies closure continuity". Glaskow Math. J. 40 (1988), 473. MR 1660074
[2] Levine N.: A decomposition of continuity in topological spaces. Amer. Math. Monthly 68 (1961), 44–46. MR 0126252 | Zbl 0100.18601
[3] Long P. E., McGehee E. E.: Properties of almost continuous functions. Proc. Amer. Math. Soc. 24 (1970), 175–180. MR 0251704 | Zbl 0186.56003
[4] Long P. E., Carnahan D. A.: Comparing almost continuous functions. Proc. Amer. Math. Soc. 38 (1973), 413–418. MR 0310824 | Zbl 0261.54007
[5] Noire T. : On weakly continuous mappings. Proc. Amer. Math. Soc. 46 (1974), 120–124. MR 0348698
[6] Saleh M.: Almost continuity implies closure continuity. Glaskow Math. J. 40 (1998), 263–264. MR 1630179 | Zbl 0898.54015
[7] Singal M. K., Singal A. R.: Almost continuous mappings. Yokohama Math. J. 16 (1968), 63–73. MR 0261569 | Zbl 0191.20802
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