On approximation of mappings with values in the space of continuous functions
| Autor: | H. A. Voloshyn, V. K. Maslyuchenko, O. N. Nesterenko |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 4, Iss 1, Pp 23-27 (2013) |
| Druh dokumentu: | article |
| ISSN: | 2075-9827 2313-0210 |
| DOI: | 10.15330/cmp.4.1.23-27 |
| Popis: | Using a theorem on the approximation of the identity in the Banach space $C_u(Y)$ of all continuous functions $g:Y\rightarrow \mathbb{R}$, defined on a metrizable compact $Y$ with the uniform norm, we prove that for a topological space $X$, a metrizable compact $Y$, a linear subspace $L$ of $Y$ dense in $C_u(Y)$ and a separately continuous function $f: X\times Y\rightarrow \mathbb{R}$ there exists a sequence of jointly continuous functions $f_n: X\times Y\rightarrow \mathbb{R}$ such that $f_n^x = f(x, \cdot)\in L$ and $f_n^x \rightarrow f^x$ in $C_u(Y)$ for each $x\in X$. |
| Databáze: | Directory of Open Access Journals |
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