An internal characterization of the Arkhangel’skiĭ-Calbrix main theorem from [4] is obtained by showing that the space \(C_{p}(X)\) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in \(\mathbb {R}^{X}\) if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is \(\sigma \) -compact if and only if X has a nice framing. We analyse a few concepts which are useful while studying nice framings. For example, a class of Tychonoff spaces X containing strictly Lindelöf Čech-complete spaces is introduced for which a variant of Arkhangel’skiĭ-Calbrix theorem for \(\sigma \)-boundedness of X is shown.

通过显示Tychonoff空间X上连续实值函数的空间\（C_ {p}（X）\）是K-解析框架而获得的，来自[4]的Arkhangel'skiĭ-Calbrix主定理的内部表征当且仅当X接受好框架时，才在\（\ mathbb {R} ^ {X} \）中。这适用于表明，当且仅当X具有良好的框架时，可量化（或宇宙）的空间X是\（\ sigma \）-紧凑的。我们分析了一些在研究框架时有用的概念。例如，一类Tychonoff空间X引入了严格包含LindelöfČech完全空间的空间，针对该空间，显示了X的\（\ sigma \）有界的Arkhangel'skiĭ-Calbrix定理的一个变体。