AMS (Mos) SUBJECT CLASSIFICATION CODES. Primary: 46A12
... concept of F-semi-norms in topological vector spaces. The details may be found in [6]. In section 3, we define the concept of partition of unity in *-inductive limit and using this, obtain a family of F--semi-norms defining the *-inductive limit topology. Finally we conclude with a representation th ...
... concept of F-semi-norms in topological vector spaces. The details may be found in [6]. In section 3, we define the concept of partition of unity in *-inductive limit and using this, obtain a family of F--semi-norms defining the *-inductive limit topology. Finally we conclude with a representation th ...
Product spaces
... If AQ and AI were separated by disjoint open sets UQ , UI ⊂ X × X, then for every point (a, −a) ∈ AQ there would have to a basis element [b, ci × [d, ei with (a, −a) ∈ [b, ci × [d, ei ⊂ UQ , and similarly for points (a, −a) ∈ AI . But the only basis elements [b, ci × [d, ei that intersect one but no ...
... If AQ and AI were separated by disjoint open sets UQ , UI ⊂ X × X, then for every point (a, −a) ∈ AQ there would have to a basis element [b, ci × [d, ei with (a, −a) ∈ [b, ci × [d, ei ⊂ UQ , and similarly for points (a, −a) ∈ AI . But the only basis elements [b, ci × [d, ei that intersect one but no ...
1.3 Pairing Function
... we can see that the pairing function is onto the set N 0, i.e. that 0 is the only atom. 1.3.3 Ordering properties of the pairing function. We have `x1 , x2 e B `y1 , y2 e x1 + x2 < y1 + y2 - x1 + x2 = y1 + y2 , x1 B y1 `x1 , x2 e < `y1 , y2 e x1 + x2 < y1 + y2 - x1 + x2 = y1 + y2 , x1 < y1 . ...
... we can see that the pairing function is onto the set N 0, i.e. that 0 is the only atom. 1.3.3 Ordering properties of the pairing function. We have `x1 , x2 e B `y1 , y2 e x1 + x2 < y1 + y2 - x1 + x2 = y1 + y2 , x1 B y1 `x1 , x2 e < `y1 , y2 e x1 + x2 < y1 + y2 - x1 + x2 = y1 + y2 , x1 < y1 . ...
