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 


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Copyright information

© Springer-Verlag New York Inc. 1982

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  • Paul R. Halmos

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