Vipul: 2 revisions

2008-05-18T19:12:40Z

2 revisions

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Vipul: Function continuously differentiable at a point moved to Function continuously real-differentiable at a point

2008-04-16T21:19:33Z

Function continuously differentiable at a point moved to Function continuously real-differentiable at a point

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Vipul: New page: {at-point function property|continuously real-differentiable function}} ==Definition== ===In one dimension over complex numbers=== Let $U \subset \mathbb{C}$ be an open subse...

2008-04-16T21:19:14Z

New page: {at-point function property|continuously real-differentiable function}} ==Definition== ===In one dimension over complex numbers=== Let <math>U \subset \mathbb{C}</math> be an open subse...

New page

{at-point function property|continuously real-differentiable function}}

==Definition==

===In one dimension over complex numbers===

Let <math>U \subset \mathbb{C}</math> be an open subset (without loss of generality, an open connected subset, i.e. a [[domain]]). Let <math>f:U \to \mathbb{C}</math> be a function, and <math>z_0 \in U</math> be a point. We say that <math>f</math> is continuously real-differentiable at <math>z_0</math> if there exists a neighborhood <math>V \ni z_0</math> such that <math>Df</math> (the Jacobian of <math>f</math> exists at all <math>z \in V</math> and each of its entries is continuous as a function of <math>z</math>.

===For maps between real vector spaces===

{{fillin}}

==Relation with other properties==

===Stronger properties===

* [[Function holomorphic at a point]]
* [[Function real-analytic at a point]]

Function continuously real-differentiable at a point - Revision history

Vipul: 2 revisions

Vipul: Function continuously differentiable at a point moved to Function continuously real-differentiable at a point

Vipul: New page: {at-point function property|continuously real-differentiable function}} ==Definition== ===In one dimension over complex numbers=== Let U \subset \mathbb{C} be an open subse...

Vipul: New page: {at-point function property|continuously real-differentiable function}} ==Definition== ===In one dimension over complex numbers=== Let $U \subset \mathbb{C}$ be an open subse...