# On normality of spaces of scatteredly continuous maps

Author B. M. Bokalo, N. M. Kolos

Lviv National University

Abstract A map $f\colon X\rightarrow Y$ between topological spaces is called scatteredly continuous if for each non-empty subspace $A\subset X$ 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.
Keywords topological spaces; pointwise convergence
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Pages 196-204
Volume 35
Issue 2
Year 2011
Journal Matematychni Studii
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