Problem:

Show that the set is pathwise connected.

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I can only think of a generalized path.

Since , then there is a parametric path consisting of two lines conneting the x-axis and y-axis. So the parametric path is and the parameteric path is dependent on the values of x, y.

If x > 0, y > 0, then

If x < 0, y < 0, then

and vice versa. However, I do not know how to prove this for all points.

Thank you for reading. Any help is greatly appreciated.