Set of continuity points of functions with values in generalized metric spaces

In: Tatra Mountains Mathematical Publications, vol. 42, no. 1

Ľubica Holá - Zbigniew Piotrowski

Detaily:

Rok, strany: 2009, 149 - 160

Kľúčové slová:

$p$-space, $G_\delta$-diagonal, developable space, weakly developable space, quasi-continuous function, generalized oscillation

Full text

O článku:

We study continuity points of functions with values in generalized metric spaces. We define the generalized oscillation, which is a useful tool in our study. Let $X$ be a topological space and $Y$ be a weakly developable space. Let $f\colon X \to Y$ be a function. Then the set $C(f)$ of continuity points of $f$ is a $G_δ$-set in $X$. Some results concerning continuity points of separately continuous functions as well as functions with closed graphs are also given.

Ako citovať:

ISO 690:

Holá, Ľ., Piotrowski, Z. 2009. Set of continuity points of functions with values in generalized metric spaces. In Tatra Mountains Mathematical Publications, vol. 42, no.1, pp. 149-160. 1210-3195.

APA:

Holá, Ľ., Piotrowski, Z. (2009). Set of continuity points of functions with values in generalized metric spaces. Tatra Mountains Mathematical Publications, 42(1), 149-160. 1210-3195.