nLab
subsets of lctvs

Lexicography of Subsets of Topological Vector Spaces

Idea

There are many different types of special subset of topological vector space. The purpose here is to list many of them, to note easy relationships between them, and to remark on their use.

Lexicography

Some of these only make sense if the vector space is the dual of some other space.

• Absorbing
• Bounded
• Bornivorous
• Closed
• Circled
• Compact
• Convex
• Equicontinuous
• Precompact
• Radial
• Weakly Compact
• Weakly Bounded
• Weakly Closed