Weak Topology

  • Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 19)


A Hilbert space is a metric space, and, as such, it is a topological space. The metric topology (or norm topology) of a Hilbert space is often called the strong topology. A base for the strong topology is the collection of open balls, i.e., sets of the form
$$ \left\{ {f:\left\| {f - {f_0}} \right\| < \varepsilon } \right\}, $$
where f0 (the center) is a vector and ε (the radius) is a positive number.


Hilbert Space Topological Space Unit Ball Weak Topology Convergent Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag New York Inc. 1982

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  • Paul R. Halmos

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