On normality of spaces of scatteredly continuous maps
A map f:X→Y between topological spaces is called scatteredly continuous if for each non-empty subspace A⊂X the restriction f| A has a point of continuity. By SC p (X) we denote the space of all scatteredly continuous real-valued functions on X endowed with the topology of pointwise convergence...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2011-05-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/texts/2011/35_2/196-204.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A map f:X→Y between topological spaces is called scatteredly continuous if for each non-empty subspace A⊂X the restriction f| A has a point of continuity. By SC p (X) we denote the space of all scatteredly continuous real-valued functions on X endowed with the topology of pointwise convergence. In this paper we focus on the normality of the space SC p (X) . Particularly, it is proved that if the function space SC p (X) is normal, then all compact and all scattered subspaces of X are countable. |
|---|---|
| ISSN: | 1027-4634 |