The order-bound topology

1972 ◽  
Vol 71 (2) ◽  
pp. 321-327 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Vector Space ◽  
Positive Cone ◽  
Order Topology ◽  
Bounded Subset ◽  
Partially Ordered ◽  
Convex Topology ◽  
Ordered Vector Space ◽  
Partially Ordered Vector Space ◽  
Locally Convex Topology ◽  
Locally Convex

Let (E, C) be a partially ordered vector space with positive cone C. The order-bound topology Pb(6) (order topology in the terminology of Schaefer(9)) on E is the finest locally convex topology for which every order-bounded subset of E is topologically bounded.

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