Theorems · Theorem · general topology

closure_lt_subset_le

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : Preorder α] [t : OrderClosedTopology α]
  [inst_2 : TopologicalSpace β] {f g : β → α}, Continuous f → Continuous g → closure {b | f b < g b} ⊆ {b | f b ≤ g b}

Defined in

Mathlib.Topology.Order.OrderClosed

Cited by

6 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpacePreorderOrderClosedTopologyTopologicalSpace