E.2 Topological Vector Spaces
... of seminorms is a topological vector space. Theorem E.21. If X is a vector space whose topology is is induced from a family of seminorms {ρα }α∈J , then X is a locally convex topological vector space. Proof. We have already seen that there is a base for the topology that consists of convex open sets ...
... of seminorms is a topological vector space. Theorem E.21. If X is a vector space whose topology is is induced from a family of seminorms {ρα }α∈J , then X is a locally convex topological vector space. Proof. We have already seen that there is a base for the topology that consists of convex open sets ...
COMPLETE METRIC ABSOLUTE NEIGHBORHOOD RETRACTS 1
... It has been proved by Sakai & Yang [8] that the Wijsman hyperspace of Rn is homeomorphic to the Hilbert cube minus a point (the authors of [8] consider hyperspaces with the Fell topology which, in the case of locally compact metric spaces, is equivalent to the Wijsman one). So the Wijsman hyperspace ...
... It has been proved by Sakai & Yang [8] that the Wijsman hyperspace of Rn is homeomorphic to the Hilbert cube minus a point (the authors of [8] consider hyperspaces with the Fell topology which, in the case of locally compact metric spaces, is equivalent to the Wijsman one). So the Wijsman hyperspace ...
Lecture 9
... U = ∅, {c}, {b, d}, {a, b, d}, {b, d, e}, {b, c, d}, {a, b, c, d}, {a, b, d, e}, {b, c, d, e}, X . It is routine, if tedious, to check that the intersection of any two elements of U is an element of U, and the union of any two elements of U is an element of U. Using this it is easy to prove by induc ...
... U = ∅, {c}, {b, d}, {a, b, d}, {b, d, e}, {b, c, d}, {a, b, c, d}, {a, b, d, e}, {b, c, d, e}, X . It is routine, if tedious, to check that the intersection of any two elements of U is an element of U, and the union of any two elements of U is an element of U. Using this it is easy to prove by induc ...
