Topological Vector Spaces

Inhaltsverzeichnis

• Strings and linear topologies.
• Metrizable topological vector spaces.
• Projective limits of topological vector spaces.
• Inductive limits of topological vector spaces.
• Topological direct sums, strict inductive limits.
• Barrelled topological vector spaces.
• The Banach-steinhaus theorem.
• Barrelled spaces and the closed graph theorem.
• Barrelled spaces and the open mapping theorem.
• Completeness and the closed graph theorem.
• Bornological spaces.
• Spaces of continuous linear mappings and their completion.
• Quasibarrelled spaces.
• Boundedly summing spaces.
• Locally topological spaces.
• Spaces with an absorbing sequence.
• ?-locally topological spaces.
• (DF)-spaces and spaces with a fundamental sequence of compact sets.
• Some examples and counter examples.