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Advanced Geometry 2020/21 Intermediate Exercises

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Advanced Geometry 2020/21 Intermediate Exercises

Esercise 1. -

a) Show that if X, Y are homeomorphic topolog- ical spaces, then X is pathwise connected if and only if Y is pathwise connected.

b) Show that any topological space X with the trivial topology is pathwise connected and also sim- ply connected.

Esercise 2. -

a) Determine a homotopy equivalence between R

4

−(plane) and R

2

−(point).

b) Show that R

4

−(plane) is not homotopy equiv-

alent to S

2

−(point).

Riferimenti

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