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Hello everyone,

Here is the definition of path connected and domain my textbook provides:

Definition 171. An open set S is path connected if each pair of points in S can be connected

by a polygonal line (e.g. a finite number of line segments connected end to end). A domain

is an open set that is path connected.

I am asked to determine whether "The set given by ##r>0##, ##- \pi < \Theta < \pi##" is path connected and is a domain.

I just want to make sure I understand exactly what the set is. Is the set they describe ##S = \{(r,\Theta)~|~r >0 \wedge \Theta \in (- \pi, \pi) \}##; and does this set consist of all the points in the complex plane, other than those along the negative real-axis?

If that's the case, it would seem as though it would be path connected.

Here is the definition of path connected and domain my textbook provides:

Definition 171. An open set S is path connected if each pair of points in S can be connected

by a polygonal line (e.g. a finite number of line segments connected end to end). A domain

is an open set that is path connected.

I am asked to determine whether "The set given by ##r>0##, ##- \pi < \Theta < \pi##" is path connected and is a domain.

I just want to make sure I understand exactly what the set is. Is the set they describe ##S = \{(r,\Theta)~|~r >0 \wedge \Theta \in (- \pi, \pi) \}##; and does this set consist of all the points in the complex plane, other than those along the negative real-axis?

If that's the case, it would seem as though it would be path connected.