- #1
Ricster55
- 39
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Right now, I am studying Advanced Calculus (proof based), and it is hard thinking through some of the definitions without first thinking about it concretely (meaning how to visualize it better geometrically, if that makes any sense?). I need help with this definition.
Definition
Let X be a metric space. A set G ⊂ X is open if for every a ∈ G there exists r > 0 such that Br(a) ⊂ G. A subset F ⊂ X is closed if F^C = X - F is open.
How do I try to "visualize" this definition, through say, a diagram or a set example?
Definition
Let X be a metric space. A set G ⊂ X is open if for every a ∈ G there exists r > 0 such that Br(a) ⊂ G. A subset F ⊂ X is closed if F^C = X - F is open.
How do I try to "visualize" this definition, through say, a diagram or a set example?