Initial Topology, Topological Vector Spaces, Weak Topology

2020 ◽  
pp. 1-9
Author(s):  
Jürgen Voigt
Keyword(s):  
Weak Topology ◽  
Vector Spaces ◽  
Topological Vector Spaces

scholarly journals On strong lifting compactness, with applications to topological vector spaces

1986 ◽  
Vol 41 (2) ◽  
pp. 211-223 ◽  
Author(s):  
A. G. A. G. Babiker ◽  
G. Heller ◽  
W. Strauss
Keyword(s):  
Structural Properties ◽  
Weak Topology ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Hausdorff Spaces ◽  
Topological Vector Spaces ◽  
Completely Regular ◽  
Locally Convex ◽  
Convex Spaces

AbstractThe notion of strong lifting compactness is introduced for completely regular Hausdorff spaces, and its structural properties, as well as its relationship to the strong lifting, to measure compactness, and to lifting compactness, are discussed. For metrizable locally convex spaces under their weak topology, strong lifting compactness is characterized by a list of conditions which are either measure theoretical or topological in their nature, and from which it can be seen that strong lifting compactness is the strong counterpart of measure compactness in that case.

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

scholarly journals *—Inductive limits and partition of unity

1989 ◽  
Vol 12 (3) ◽  
pp. 429-434
Author(s):  
V. Murali
Keyword(s):  
Inductive Limit ◽  
Partition Of Unity ◽  
Vector Spaces ◽  
Inductive Limits ◽  
Topological Vector Spaces ◽  
Limit Space ◽  
Direct Sum

In this note we define and discuss some properties of partition of unity on *-inductive limits of topological vector spaces. We prove that if a partition of unity exists on a *-inductive limit space of a collection of topological vector spaces, then it is isomorphic and homeomorphic to a subspace of a *-direct sum of topological vector spaces.

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