# Do you know Topology?

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

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