cardinality of set of all real continuous functions

Asked Jan 06 '13 at 16:51

Active Sep 03 '14 at 06:47

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Could somebody explain to me how to prove that the cardinality of all real continuous functions is $c$ ?

The first problem is that I don't know how to show that each real continuous function $f: X \rightarrow Y$ is uniquely determined by its values for $x \in Q $.

Secondly, how to show that $R^Q \sim R^N \sim R$ ?

Thank you.

edited Sep 03 '14 at 06:25

Martin Sleziak

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asked Jan 06 '13 at 16:51

Bilbo

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See Cardinality of set of real continuous functions and Can there be two distinct, continuous functions that are equal at all rationals?. – Martin Sleziak Jan 07 '13 at 06:34

cardinality of set of all real continuous functions

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