seqClosure_subset_closure — Mathlib

English

If a set s is sequentially closed, then its sequential closure equals s.

Русский

Если множество s последовательности замкнуто, то seqClosure(s) = s.

LaTeX

$$$ \text{IsSeqClosed}(s) \Rightarrow \mathrm{seqClosure}(s) = s $$$

Lean4

/-- The sequential closure of a set is contained in the closure of that set.
The converse is not true. -/
theorem seqClosure_subset_closure {s : Set X} : seqClosure s ⊆ closure s := fun _p ⟨_x, xM, xp⟩ =>
  mem_closure_of_tendsto xp (univ_mem' xM)

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