# Do you know Topology?

**Discrete Mathematics**Level 4

**How many statements below are true?**

1.- There exists a homeomorphism (bijective continuous function) from [-1,1] to (-1,1)

2.- There exists a homeomorphism from \(\mathbb {R}^2\) to \(\mathbb {R}\)

3.- There exists a homeomorphism from (-1,1) to \(\mathbb {R}\)

4.- There exists a homeomorphism from \(\mathbb {R}^2\) to \(\mathbb {R}^2 \) - {0}

**Details and assumptions**

The toplogy in each space,subspace is the usual or euclidean topology