<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 <italic>X </italic>be a topological space and <italic>Y </italic>be a weakly developable space. Let ƒ</p><p><italic></italic>: <italic>X </italic>→<italic>Y </italic>be a function. Then the set <italic>C </italic>(ƒ) of continuity points of ƒ<italic></italic>is a <italic>Gδ</italic>-set in <italic>X</italic>. Some results concerning continuity points of separately continuous functions as well as functions with closed graphs are also given.</p></abstract>

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 ƒ: X →Y be a function. Then the set C (ƒ) of continuity points of ƒis a Gδ-set in X. Some results concerning continuity points of separately continuous functions as well as functions with closed graphs are also given.

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

Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814-73 Bratislava SLOVAKIA

Department of Mathematics Youngstown State University Youngstown, Ohio 44555-0001 U.S.A.

Tatra Mountains Mathematical Publications

{"article-title":"Set of continuity points of functions with values in generalized metric spaces"}

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....

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

Publié en ligne: 12 nov. 2012

Pages: 149 - 160

DOI: https://doi.org/10.2478/v10127-009-0014-9

Mots clés
p-space, Gδ-diagonal, developable space, weakly developable space, quasicontinuous function, generalized oscillation

This content is open access.

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

Publié en ligne: 12 nov. 2012

Pages: 149 - 160

DOI: https://doi.org/10.2478/v10127-009-0014-9

Mots clésp-space, Gδ-diagonal, developable space, weakly developable space, quasicontinuous function, generalized oscillation

This content is open access.

Mots clés
p-space, Gδ-diagonal, developable space, weakly developable space, quasicontinuous function, generalized oscillation