Question

In: Advanced Math

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the...

1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the subspace topology given by τs.

2. Let f: X → Y continue. We say that f is open if it sends open of X in open of Y. Show that the canonical projection

ρi: X1 × X2 → Xi
(x1, x2) −→ xi

It is continuous and open, for i = 1, 2, where (X1, τ1) and (X2, τ2) are two topological spaces and X1 × X2 has the product topology.

Solutions

Expert Solution

We are proving this theorem for rho11). Let X = ( a, b) be an inetval . To prove that X is connected.

Colby Messinger answered 1 year ago
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