$Let \;$ = $\{(, ) ∈ ℝ^2: ^2 + ^2 = 1\} \bigcup([−1,1] × {0}) ∪ ({0} × [−1,1]).$
Let$\; _0$ = $\max\{ ∶ < ∞,$ there are$\; $ distinct points$\; _1, … , _ ∈ $ such that $\setminus \{_1, … , _ \}$ is connected$\}$
1). The value of $_0$ is
2).Let $\{ _1,\dots, _{n_{{0}+1}}\}$ be $ _{0+1}$ distinct points and $ = \setminus\{_1, … ,_{n_{0}+1}\}$. Let $$ be the number of connected components of $$. The maximum possible value of $$ is ______
The diagram of a given set is like $\bigoplus$ , if remove the corner pints $(1,0),(-1,0),(0,1),(0,-1)$ then the is the set I got connected? I don't know how to approch the answer, I know the definition of connected set but how to apply that definition here?
Please, help.
Thank you.