Commutative Diagram/Examples/Square Function with Square Root
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Example of Commutative Diagram
Let $g$ and $h$ be the real functions defined as:
- $\forall x \in \R: \map g x = x^2$
- $\forall x \in \R_{\ge 0}: \map h x = \sqrt x$
The composition $h \circ g$ can be depicted using a commutative diagram as follows:
$\quad\quad\begin{xy} \xymatrix@L+2mu@+1em{ \R \ar[r]^*{g} \ar@{-->}[rd]_*{h \circ g} & \R_{\ge 0} \ar[d]^*{h} \\ & \R_{\ge 0} }\end{xy}$
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 8$: Composition of Functions and Diagrams: Exercise $1$