![Extension and Selection theorems in Topological spaces](http://s1.studyres.com/store/data/001715110_1-8dc931307bfb28ef78ec7bb6b8b0964e-300x300.png)
... Here f : (X,τ1, G1) → (Y,τ2, G2) is a almost homeomorphism mapping of an G1-NC space X on to Y. Let U ={Uα : α ∈ Λ} be any regular open cover of Y. Then f being almost continuous, U* ={f −1(Uα) : α ∈ Λ} is an open cover of the G1-NC space X. Therefore there exists a finite subfamily, {f −1(Uα ) : i ...
Scheme representation for first-order logic
... model) can be interpreted as the set of T-model homomorphisms mapping into M. Every formula ϕ(x1 , . . . , xn ) determines a “definable sheaf” [[ϕ]] over the spectrum. Over each model M , the fiber of [[ϕ]] is the definable set stalkM ([[ϕ]]) = ϕM = {a ∈ |M |n | M |= ϕ(a)}. The space [[ϕ]] is topolo ...
... model) can be interpreted as the set of T-model homomorphisms mapping into M. Every formula ϕ(x1 , . . . , xn ) determines a “definable sheaf” [[ϕ]] over the spectrum. Over each model M , the fiber of [[ϕ]] is the definable set stalkM ([[ϕ]]) = ϕM = {a ∈ |M |n | M |= ϕ(a)}. The space [[ϕ]] is topolo ...