View source for Real-valued function

==Definition==
A ''[[function]]'' is said to be ''real-valued'' if the [[co-domain]] is the set of [[real numbers]], {{M|\mathbb{R} }}<ref name="ITSM">Introduction to Smooth Manifolds - Second Edition - John M. Lee - Springer GTM</ref>. That is to say any function ( {{M|f}} ) and any set ( {{M|U}} ) such that:
* {{M|f:U\rightarrow\mathbb{R} }}
==See also==
* [[Extended-real-valued function]]
* [[Extended real value|Extended-real-value]]
* [[Class of smooth real-valued functions on R-n|The class of smooth real-valued functions on {{M|\mathbb{R}^n}}]]
* [[Class of k-differentiable real-valued functions on R-n|The class of {{M|k}}-differentiable real-valued functions on {{M|\mathbb{R}^n}}]]
==References==
<references/>
{{Definition|Measure Theory|Manifolds|Differential Geometry|Functional Analysis}}