Disk compactness

Question

$$\mathring{D}_2 = \{(x, y) \in \mathbb{R}^2 \mid x^2 + y^2 < 1\}$$ Is this compact? What is an example of a open covering if it isn't compact? What does the dot on top of the Disk mean?

Answer 1

JW Tanner points out how it is not compact. Please typeset questions with MathJax for future reference. The dot on top denotes "interior", a topological concept you can look up. The idea is that one generally denotes $D^2:= \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \leq 1\}$. Then $\mathring{D^2}$ would then be as you define it, if you take the topological interior of $D^2$.