On the completion of a bornological space

1977 ◽  
Vol 29 (1) ◽  
pp. 608-613 ◽  
Author(s):  
M. Valdivia
Keyword(s):  
Bornological Space

scholarly journals BORNOLOGICAL COUNTABLE ENLARGEMENTS

2003 ◽  
Vol 46 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Ian Tweddle ◽  
S. A. Saxon
Keyword(s):  
Subject Classification ◽  
Bornological Space ◽  
Mackey Topologies

AbstractWe show that for a non-flat bornological space there is always a bornological countable enlargement; moreover, when the space is non-flat and ultrabornological the countable enlargement may be chosen to be both bornological and barrelled. It is also shown that countable enlargements for barrelled or bornological spaces are always Mackey topologies, and every quasibarrelled space that is not barrelled has a quasibarrelled countable enlargement.AMS 2000 Mathematics subject classification: Primary 46A08; 46A20

scholarly journals Stability and closed graph theorems in classes of bornological spaces

1982 ◽  
Vol 23 (2) ◽  
pp. 151-162
Author(s):  
T. K. Mukherjee ◽  
W. H. Summers
Keyword(s):  
Inductive Limit ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Closed Graph ◽  
Quotient Spaces ◽  
Direct Sum ◽  
Bornological Space ◽  
Normed Vector ◽  
Locally Convex

In the general theory of locally convex spaces, the idea of inductive limit is pervasive, with quotient spaces and the less obvious notion of direct sum being among the instances. Bornological spaces provide another important example. As is well known (cf. [7]), a Hausdorff locally convex space E is bornological if, and only if, E is an inductive limit of normed vector spaces. Going even further in this direction, a complete Hausdorff bornological space is an inductive limit of Banach spaces.

scholarly journals Semi Compactness Space in Bornological Space

2019 ◽  
Vol 15 (4) ◽  
pp. 101-107
Author(s):  
Huda Abd Ameer
Keyword(s):  
Bornological Space

scholarly journals Semiconvex spaces II

1969 ◽  
Vol 10 (2) ◽  
pp. 103-105 ◽  
Author(s):  
S. O. Iyahen
Keyword(s):  
Measure Theory ◽  
Classical Case ◽  
Bornological Space

One of the concepts introduced in [2] is that of a hyperbornological space, an idea which effectively replaces that of a bornological space when semiconvex spaces are being considered. In Section 2 of the present paper, it is shown how the topology of such a space may be described in terms of bounded pseudometrices. This is used in Section 3 to tackle the problem of when a product of separated hyperbornological spaces has the same property. It is shown that, as in the classical case of bornological spaces, this problem is equivalent to one in measure theory.

scholarly journals Duality properties of spaces of non-Archimedean valued functions

1987 ◽  
Vol 42 (1) ◽  
pp. 48-56
Author(s):  
W. Govaerts
Keyword(s):  
Uniform Convergence ◽  
Compact Hausdorff Space ◽  
Convex Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Complete Characterization ◽  
Bornological Space ◽  
Valued Field ◽  
Better Than

AbstractLet C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).

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