basicOpen_eq_bot_iff_forall_evaluation_eq_zero

English

The same characterization as above in terms of the bottom element of the lattice of opens.

Русский

Та же характеристика через нижний элемент решетки открытых множеств.

LaTeX

$$$$ X.\mathrm{basicOpen}(f) = \top \text{ or bottom?} $$$$

Lean4

theorem basicOpen_eq_bot_iff_forall_evaluation_eq_zero (f : X.presheaf.obj (op U)) :
    X.basicOpen f = ⊥ ↔ ∀ (x : U), X.evaluation U x x.property f = 0 :=
  X.toLocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero f

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