- #1

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## Homework Statement

No problem statement

## Homework Equations

## The Attempt at a Solution

Let ##A = \{(x,y) ~|~ x \ge 0 \mbox{ or } y=0 \}## be a subspace, which can be shown closed, of ##\Bbb{R}^2##. If my calculations are right, isn't ##A \cap [(0,\infty) \times \Bbb{R} ] = (\{0\} \times \Bbb{R}) \cup ((0,\infty) \times \{0\})## and therefore ##\pi_1(A \cap [(0,\infty) \times \Bbb{R} ] ) = [0,\infty)##, where ##\pi_1 : \Bbb{R}^2 \to \Bbb{R}## the canonical projection map onto the first coordinate, thereby showing that ##\pi_1## restricted to ##A## is not an open map?