Open set
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Here (X,d) denotes a metric space, and Br(x) the open ball centred at x of radius r
Metric Space definition
"A set U is open if it is a neighborhood to all of its points"[1] and neighborhood is as you'd expect, "a small area around".
Neighborhood
A set N is a neighborhood to a∈X
if ∃δ>0:Bδ(a)⊂N
- Jump up ↑ Bert Mendelson, Introduction to Topology - definition 6.1, page 52
