I'm having trouble looking for a guideline on how to prove a set is open/closed:
Show that $A = \{(x,y) \in \mathbb{R}^{2} \mid x^{2} + y + 2x = 3\}$ is closed by showing that every limit point of A is in A.
a) Let $S = \{x \in \mathbb{R} \mid x \not\in \mathbb{Q}\}$, is S closed?
b) Show that $S = \{(x,y) \in \mathbb{R}^{2} \mid xy > 0\}$ is open
c) Let $A,B \subset \mathbb{R}$ with $A$ open, and defined $AB = \{xy \mid (x \in A)\wedge(y \in B)\}$, is $AB$ necessarily open?
Please help me. Thanks!