Difference between revisions of "Real-valued function"
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==See also== | ==See also== | ||
* [[Extended-real-valued function]] | * [[Extended-real-valued function]] | ||
| − | * [[Class of smooth real-valued functions|The class of smooth real-valued functions]] | + | * [[Extended real value|Extended-real-value]] |
| − | * [[Class of k-differentiable real-valued functions|The class of {{M|k}}-differentiable real-valued functions]] | + | * [[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== | ||
<references/> | <references/> | ||
{{Definition|Measure Theory|Manifolds|Differential Geometry|Functional Analysis}} | {{Definition|Measure Theory|Manifolds|Differential Geometry|Functional Analysis}} | ||
Latest revision as of 23:15, 21 October 2015
Definition
A function is said to be real-valued if the co-domain is the set of real numbers, [ilmath]\mathbb{R} [/ilmath][1]. That is to say any function ( [ilmath]f[/ilmath] ) and any set ( [ilmath]U[/ilmath] ) such that:
- [ilmath]f:U\rightarrow\mathbb{R} [/ilmath]
See also
- Extended-real-valued function
- Extended-real-value
- The class of smooth real-valued functions on [ilmath]\mathbb{R}^n[/ilmath]
- The class of [ilmath]k[/ilmath]-differentiable real-valued functions on [ilmath]\mathbb{R}^n[/ilmath]
References
- ↑ Introduction to Smooth Manifolds - Second Edition - John M. Lee - Springer GTM
