Section 8.3 Powerpoint
... San Francisco, California, is famous for its steep streets. The steepness of a road is often expressed as a percent grade. Filbert Street, the steepest street in San Francisco, has a 31.5% grade. This means the road rises 31.5 ft over a horizontal distance of 100 ft, which is equivalent to a 17.5° a ...
... San Francisco, California, is famous for its steep streets. The steepness of a road is often expressed as a percent grade. Filbert Street, the steepest street in San Francisco, has a 31.5% grade. This means the road rises 31.5 ft over a horizontal distance of 100 ft, which is equivalent to a 17.5° a ...
Loesungen - Institut für Mathematik
... neighborhoods Ux and Vy of x and y respectively, such that Ux ∩ Vy = ∅. Therefore (Ux × Vy ) ∩ ∆ = ∅. It follows that (x, y) ∈ Ux × Vy ⊂ (X × X) \ ∆, so that ∆ is closed. Exercise 4 (8 points) Let X be a topological space. For any x ∈ X let C(x) be the connected component of X containing x. Recall f ...
... neighborhoods Ux and Vy of x and y respectively, such that Ux ∩ Vy = ∅. Therefore (Ux × Vy ) ∩ ∆ = ∅. It follows that (x, y) ∈ Ux × Vy ⊂ (X × X) \ ∆, so that ∆ is closed. Exercise 4 (8 points) Let X be a topological space. For any x ∈ X let C(x) be the connected component of X containing x. Recall f ...
Branched covers of the Riemann sphere
... an open map, by the open mapping theorem in complex analysis (or more concretely, because the map z 7→ z e is visibly open for any e). Then for any open subset U 0 ⊆ CP1 , the induced map f −1 (U 0 ) → U 0 is also open and closed. It follows that if W ⊆ f −1 (U 0 ) is a connected component, its imag ...
... an open map, by the open mapping theorem in complex analysis (or more concretely, because the map z 7→ z e is visibly open for any e). Then for any open subset U 0 ⊆ CP1 , the induced map f −1 (U 0 ) → U 0 is also open and closed. It follows that if W ⊆ f −1 (U 0 ) is a connected component, its imag ...
