# Wankuri Rar

wankuri es \b7\w+\w?\S?\b .Q: Continuous Mapping Lemma In reading about continuous mapping I have seen the following statement: If $g$ is a continuous mapping of $X$ into a complete metric space $Y$ and $f: Y\rightarrow Z$ is a mapping into a metric space, then $f\circ g$ is also continuous. Here is a link to the book that I am referencing A: Let $f\colon Y \to Z$ be a mapping into a metric space and let $g \colon X\to Y$ be continuous. For each $y\in Y$ we have $d_Z(g(x), g(x^{\prime})) \leq d_Y(y,y^\prime)$ for all $x,x^\prime \in X$ and thus $g(x) \in \operatorname{im} f \quad \forall x \in X$ We know that the image of $g \colon X \to Y$ is closed, because $X$ is complete, $g$ is continuous, and $Y$ is complete. Hence, the image of $f\circ g \colon X \to Z$ is closed. The image of $g \colon X \to Y$ is closed because the image of every function with closed image is closed. The image of $f\circ g \colon X \to Z$ is closed because $\operatorname{im} f$ is closed and $Z$ is complete. If $f$ has closed image, the continuity of $f$ is equivalent to the continuity of $f\circ g$. }“, common.Pkg.Config.Data.Deps[localName]), pkg_${localName} = require(„${common.Pkg.Config.Data.Deps[localName]}“) ); } else { module.exports.syncModules[localName] 04aeff104c