On uniform deviation from the space of continuous function

• Datum: 2014
• Hauptverfasser: Maslyuchenko, V. K., Mel’nyk, V. S., Маслюченко, В. К., Мельник, В. С.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут математики НАН України 2014
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/74
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

It's proven that for the normal space $X$ and any function $f\!:X\!\rightarrow\!\mathbb{R}$ the uniform distance $d(f,C(X))$ of function $f$ from the space $C(X)$ of all continuous functions $g\!:X\!\rightarrow \!\mathbb{R}$ is equal to the half of the uniform norm $\|\omega_{f}\|$ of the f...