tendsto_norm_one — Mathlib

English

If two elements u and v in E are inseparable, their norms are equal: ‖u‖ = ‖v‖.

Русский

Если два элемента u и v в E неразделимы, то их нормы равны: ‖u‖ = ‖v‖.

LaTeX

$$$ \text{Inseparable}(u,v) \implies \|u\| = \|v\|. $$$

Lean4

/-- See `tendsto_norm_one` for a version with pointed neighborhoods. -/
@[to_additive /-- See `tendsto_norm_zero` for a version with pointed neighborhoods. -/
    ]
theorem tendsto_norm_one : Tendsto (fun a : E => ‖a‖) (𝓝 1) (𝓝 0) := by simpa using tendsto_norm_div_self (1 : E)

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