LH has nonempty products
نویسنده
چکیده
Definition For an element x of a topological space X , we will write Ux for the set of all open neigborhoods of x. f : X → Y is a local homeomorphism if for every x ∈ X there exists a U ∈ Ux such that f |U is a homeomorphism onto an open subset of Y . Denote by intA the interior of A ⊆ X . For any pair of maps φ : U → Y , φ : V → Y defined on open subsets U, V ⊆ X , define the (set) equalizer eq(φ, φ) := {x ∈ U ∩ V | φ(x) = φ(x)}. In the following, we will only consider open equalizers int eq(φ, φ).
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