Convergence_in_Indiscrete_Space

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Let \left({S, \left\\right) be an indiscrete space. Let $\left \langle {x_n} \right \rangle$ be any sequence in $S$. Then $\left \langle {x_n} \right \rangle$ converges to any point $x$ of $S$.

Why this node was retired

The posted statement is

theorem Convergence_in_Indiscrete_Space {α : Type _} (x : α) (f : ℕ → α) : @Filter.Tendsto _ _ f Filter.atTop (@nhds α ⊥ x) := by sorry

The topology is ⊥, which is discrete in Mathlib’s reverse lattice order.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Replace @nhds α ⊥ x by @nhds α ⊤ x; every sequence converges to every point in the indiscrete topology.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.