# 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

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topPetalas, 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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- Noire T., On weakly continuous mappings, Proc. Amer. Math. Soc. 46 (1974), 120–124. (1974) MR0348698
- Saleh M., Almost continuity implies closure continuity, Glaskow Math. J. 40 (1998), 263–264. (1998) Zbl0898.54015MR1630179
- Singal M. K., Singal A. R., Almost continuous mappings, Yokohama Math. J. 16 (1968), 63–73. (1968) Zbl0191.20802MR0261569

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