Topological Linear Spaces, Convex Sets, Weak Topologies

1972 ◽  
pp. 11-20
Author(s):  
Igor Vladimirovich Girsanov ◽  
B. T. Poljak
Keyword(s):  
Convex Sets ◽  
Linear Spaces ◽  
Weak Topologies ◽  
Topological Linear

scholarly journals The differentiability of convex functions on topological linear spaces

1990 ◽  
Vol 42 (2) ◽  
pp. 201-213 ◽  
Author(s):  
Bernice Sharp
Keyword(s):  
Convex Functions ◽  
Inductive Limit ◽  
Asplund Space ◽  
Fréchet Spaces ◽  
Linear Spaces ◽  
Asplund Spaces ◽  
Continuous Convex Function ◽  
Mazur’S Theorem ◽  
Topological Linear ◽  
Differentiability Properties

In this paper topological linear spaces are categorised according to the differentiability properties of their continuous convex functions. Mazur's Theorem for Banach spaces is generalised: all separable Baire topological linear spaces are weak Asplund. A class of spaces is given for which Gateaux and Fréchet differentiability of a continuous convex function coincide, which with Mazur's theorem, implies that all Montel Fréchet spaces are Asplund spaces. The effect of weakening the topology of a given space is studied in terms of the space's classification. Any topological linear space with its weak topology is an Asplund space; at the opposite end of the topological spectrum, an example is given of the inductive limit of Asplund spaces which is not even a Gateaux differentiability space.

Total Lattices of Convex Sets and of Linear Spaces

1948 ◽  
Vol 49 (3) ◽  
pp. 659 ◽  
Author(s):  
Walter Prenowitz
Keyword(s):  
Convex Sets ◽  
Linear Spaces

Fuzzifying topological linear spaces

2004 ◽  
Vol 147 (2) ◽  
pp. 249-272 ◽  
Author(s):  
Daowen Qiu
Keyword(s):  
Linear Spaces ◽  
Topological Linear
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