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1.- Prove the intermediate value theorem: let (X, τ) be a connected topological space, f: X...

1.- Prove the intermediate value theorem: let (X, τ) be a connected topological space, f: X - → Y a continuous transformation and x1, x2 ∈ X with a1 = f (x1), a2 = f (x2) ( a1 different a2). Then for all c∈ (a1, a2) there is x∈ such that f (x) = c.

2.- Let f: X - → Y be a continuous and suprajective transformation. Show that if X is connected, then Y too.

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