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typedef inside class

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I looked into my C++ standard book but couldn't find anything specific to this situation (in the "typedef" section)

class A
typedef char MyType; // intendedly private

class B : public A

typedef float MyType;

void PrintSize()
printf("%d", sizeof(MyType)); // prints 4, ok
printf("%d", sizeof(A::MyType)); // prints 1, ok

What would be the standard here?
1) Is "Overriding" a typedef from a base class permitted at all? (visual studio accepts it)
2) If it is, does it follow the usual rules of overriding? (say, like a class member)

What do you think?

Thanks for your help.

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