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On normality of spaces of scatteredly continuous maps |
| Author |
B. M. Bokalo, N. M. Kolos
Lviv National University
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| 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.
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| Keywords |
topological spaces; pointwise convergence |
| DOI |
doi:10.30970/ms.35.2.196-204
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| Reference |
1. Engelking R. General Topology. – PWN, Warzawa, 1977.
2. Bokalo B., Kolos N. When does $SC_p(X)=\mathbb{R}^X$ hold?// Topology – 2009. – V.48. – P. 178–181.
3. Arkhangel’skii A.V. Topological spaces of functions. – M.: MGU, 1989. (in Russian)
4. Arkhangel’skii A.V., Bokalo B.M. The tangency of topologies and tangential properties of topological
spaces// Trudy Moskov. Mat. Obshch. – 1992. – V.54. – P. 160–185, 278–279. (in Russian)
5. Banakh T., Bokalo B. On scatteredly continuous maps between topological spaces// Topology and Appl. –
2010. – V.157. – P. 108–122.
6. Aleksandrov P.S., Proskuryakov I.V. On reducible sets// Izv. Akad. Nauk SSSR, Ser. Mat. – 1941. – V.5,
№3. – P. 217–224. (in Russian)
7. Choban M.M., Dodon N.K. Theory of P-scattered spaces. – Stiintsa, Kishinev, 1979. (in Russian)
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| Pages |
196-204 |
| Volume |
35 |
| Issue |
2 |
| Year |
2011 |
Journal |
Matematychni Studii |
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