Differentiable vector-valued functions from Euclidean space: Difference between revisions

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{{Short description|Differentiable function in functional analysis}}

{{one source|date=January 2025}}

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In the mathematical discipline of [[functional analysis]], a '''differentiable vector-valued function from Euclidean space''' is a [[differentiable]] function valued in a [[topological vector space]] (TVS) whose [[Domain of a function|domains]] is a subset of some [[Dimension (vector space)|finite-dimensional]] [[Euclidean space]].

It is possible to generalize the notion of [[Derivative (mathematics)|derivative]] to functions whose ___domain and codomain are subsets of arbitrary [[topological vector space]]s (TVSs) in multiple ways.

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* {{annotated link|Convenient vector space}}

* {{annotated link|Crinkled arc}}

* {{annotated link|Differentiation in Fréchet spaces}}

* {{annotated link|Fréchet derivative}}

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* {{Wong Schwartz Spaces, Nuclear Spaces, and Tensor Products}} <!-- {{sfn|Wong|1979|p=}} -->

{{Functional Analysis in topological vector spaces}}

{{Topological vector spaces}}

{{TopologicalVectorSpaces}}

{{Functional analysis}}

{{AnalysisInTopologicalVectorSpaces}}

<!--- Categories --->

{{DEFAULTSORT:Differentiable vector-valued functions from Euclidean space}}

[[Category:Functions and mappings]]

[[Category:Banach spaces]]

[[Category:Differential calculus]]

[[Category:Euclidean geometry]]

[[Category:Functions and mappings]]

[[Category:Generalizations of the derivative]]

[[Category:Topological vector spaces]]