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  3. 1.- show that (r, Ï„s) is connected. also show

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

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Advance Math

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

2. Let f: X → Y continue. We say that f is open if it sends openof 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 producttopology.

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