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Function Types: continuous, surjective, injective, bijective, continuous surjective, continuous injective, continuous bijective. Then all of the above -- with each possible type of inverse?
What is possible with F:X-->Y where X, Y can be [0,1], (0,1), [0,1), Q, R, N?
I certainly don't expect a full listed answer for each combination, but some general principles would be great. :)
I already know there couldn't be bijections between sets of different cardinality. And I know there couldn't be an injection from greater to lower, or a surjection from smaller to greater cardinality.
Thanks
David
What is possible with F:X-->Y where X, Y can be [0,1], (0,1), [0,1), Q, R, N?
I certainly don't expect a full listed answer for each combination, but some general principles would be great. :)
I already know there couldn't be bijections between sets of different cardinality. And I know there couldn't be an injection from greater to lower, or a surjection from smaller to greater cardinality.
Thanks
David