A nonalgebraic approach to the theory of linear topological spaces

✍ Scribed by David C. Kay

• Publisher: Springer
• Year: 1977
• Tongue: English
• Weight: 596 KB
• Volume: 6
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147781

✦ Synopsis

The basic theory developed in the setting of an algebraic system endowed with a topology which renders the operations continuous (e.g. a topological linear space) can be produced entirely by geometric (set-theoretic) notions without using algebra. This theory affords an interesting synthesis of classical results, and is more general. For example, our theory applies to a larger class of spaces than linear topological spaces, but is powerful enough to prove the appropriate formulation in this setting of the Krein-Milman theorem on extreme points. This theorem is the goal of this particular article, as an example of the direction which the theory can be made to take.