# Cardinality/Function Question

1. Sep 20, 2010

### ded8381

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

2. Sep 21, 2010

Specifying, for instance [0,1), is not enough. You need to specify the topology. The same set can be equipped with different topologies.

3. Sep 21, 2010

### VeeEight

I'm assuming he means the standard Euclidean topology

4. Sep 21, 2010