@@ -334060,16 +334060,16 @@ or are almost disjoint (the interiors are disjoint). (Contributed by
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if ( z = x , y , ( f ` z ) ) ) e.
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( ( ( j |`t ( dom f u. { x } ) ) CnP j ) ` x ) } ) $.
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- $( Define the derivative operator on functions on the reals . This acts on
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- functions to produce a function that is defined where the original
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- function is differentiable, with value the derivative of the function at
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- these points. The set ` s ` here is the ambient topological space under
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- which we are evaluating the continuity of the difference quotient.
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- Although the definition is valid for any subset of ` CC ` and is
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- well-behaved when ` s ` contains no isolated points, we will restrict
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- our attention to the cases ` s = RR ` or ` s = CC ` for the majority of
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- the development, these corresponding respectively to real and complex
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- differentiation. (Contributed by Mario Carneiro, 7-Aug-2014.) $)
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+ $( Define the derivative operator. This acts on functions to produce a
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+ function that is defined where the original function is differentiable,
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+ with value the derivative of the function at these points. The set
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+ ` s ` here is the ambient topological space under which we are
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+ evaluating the continuity of the difference quotient. Although the
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+ definition is valid for any subset of ` CC ` and is well-behaved when
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+ ` s ` contains no isolated points, we will restrict our attention to the
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+ cases ` s = RR ` or ` s = CC ` for the majority of the development,
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+ these corresponding respectively to real and complex differentiation.
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+ (Contributed by Mario Carneiro, 7-Aug-2014.) $)
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df-dv $a |- _D = ( s e. ~P CC , f e. ( CC ^pm s ) |->
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U_ x e. ( ( int ` ( ( TopOpen ` CCfld ) |`t s ) ) ` dom f )
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( { x } X. ( ( z e. ( dom f \ { x } ) |->
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