A characterization of almost continuity and weak continuity

Chrisostomos Petalas; Theodoros Vidalis

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 133-136
  • ISSN: 0231-9721

Abstract

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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 .

How to cite

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Petalas, Chrisostomos, and Vidalis, Theodoros. "A characterization of almost continuity and weak continuity." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 133-136. <http://eudml.org/doc/32354>.

@article{Petalas2004,
abstract = {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 $X$.},
author = {Petalas, Chrisostomos, Vidalis, Theodoros},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {almost continuous function; weakly continuous function; almost continuous function; weakly continuous function},
language = {eng},
number = {1},
pages = {133-136},
publisher = {Palacký University Olomouc},
title = {A characterization of almost continuity and weak continuity},
url = {http://eudml.org/doc/32354},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Petalas, Chrisostomos
AU - Vidalis, Theodoros
TI - A characterization of almost continuity and weak continuity
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 133
EP - 136
AB - 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 $X$.
LA - eng
KW - almost continuous function; weakly continuous function; almost continuous function; weakly continuous function
UR - http://eudml.org/doc/32354
ER -

References

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  1. Dontchev J., Noiri T., A note on Saleh’s paper “Almost continuity implies closure continuity", Glaskow Math. J. 40 (1988), 473. (1988) MR1660074
  2. Levine N., A decomposition of continuity in topological spaces, Amer. Math. Monthly 68 (1961), 44–46. (1961) Zbl0100.18601MR0126252
  3. Long P. E., McGehee E. E., Properties of almost continuous functions, Proc. Amer. Math. Soc. 24 (1970), 175–180. (1970) Zbl0186.56003MR0251704
  4. Long P. E., Carnahan D. A., Comparing almost continuous functions, Proc. Amer. Math. Soc. 38 (1973), 413–418. (1973) Zbl0261.54007MR0310824
  5. Noire T., On weakly continuous mappings, Proc. Amer. Math. Soc. 46 (1974), 120–124. (1974) MR0348698
  6. Saleh M., Almost continuity implies closure continuity, Glaskow Math. J. 40 (1998), 263–264. (1998) Zbl0898.54015MR1630179
  7. Singal M. K., Singal A. R., Almost continuous mappings, Yokohama Math. J. 16 (1968), 63–73. (1968) Zbl0191.20802MR0261569

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