Strict Ball (狭義球) (Definition III.6.1)
- Strict Ball (狭義球) (Definition III.6.1) #Card
- If $d$ is a metric on $X$ and $\varepsilon > 0$, then $B(x, \varepsilon) = B_d(x, \varepsilon) := {y \in X : d(x,y) < \varepsilon}$ is called a strict ball of radius $\varepsilon$ centered at $x$.
If $d$ is a metric on $X$ and $\varepsilon > 0$, then the set $$B(x, \varepsilon) = B_d(x, \varepsilon) := {y \in X : d(x,y) < \varepsilon}$$ is called a strict ball of radius $\varepsilon$ centered at $x$.
- 離散距離 $i_X$ では $B_{i_X}(x, \varepsilon) = {x}$（$\varepsilon < 1$）、$= X$（$\varepsilon \geq 1$）。
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