Previous |  Up |  Next


Title: A characterization of almost continuity and weak continuity (English)
Author: Petalas, Chrisostomos
Author: Vidalis, Theodoros
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 43
Issue: 1
Year: 2004
Pages: 133-136
Summary lang: English
Category: math
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 $X$. (English)
Keyword: almost continuous function
Keyword: weakly continuous function
MSC: 54C08
MSC: 54C10
idZBL: Zbl 1064.54025
idMR: MR2124610
Date available: 2009-08-21T12:54:55Z
Last updated: 2012-05-04
Stable URL:
Reference: [1] Dontchev J., Noiri T.: A note on Saleh’s paper “Almost continuity implies closure continuity".Glaskow Math. J. 40 (1988), 473. MR 1660074
Reference: [2] Levine N.: A decomposition of continuity in topological spaces.Amer. Math. Monthly 68 (1961), 44–46. Zbl 0100.18601, MR 0126252
Reference: [3] Long P. E., McGehee E. E.: Properties of almost continuous functions.Proc. Amer. Math. Soc. 24 (1970), 175–180. Zbl 0186.56003, MR 0251704
Reference: [4] Long P. E., Carnahan D. A.: Comparing almost continuous functions.Proc. Amer. Math. Soc. 38 (1973), 413–418. Zbl 0261.54007, MR 0310824
Reference: [5] Noire T. : On weakly continuous mappings.Proc. Amer. Math. Soc. 46 (1974), 120–124. MR 0348698
Reference: [6] Saleh M.: Almost continuity implies closure continuity.Glaskow Math. J. 40 (1998), 263–264. Zbl 0898.54015, MR 1630179
Reference: [7] Singal M. K., Singal A. R.: Almost continuous mappings.Yokohama Math. J. 16 (1968), 63–73. Zbl 0191.20802, MR 0261569


Files Size Format View
ActaOlom_43-2004-1_13.pdf 250.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo