1981•International Journal of ControlRequires access

Extended spaces and the resolution topology†

Avraham Feintuch, Richard E. Saeks

Abstract

The extended L 2e space used to define stability and instability for systems defined on an L 2 space is shown to be the completion of the given L 2 space in an appropriate topology. This, in turn, allows the extended space concept to be generalized to an arbitrary Hilbert resolution space by taking its completion in the appropriate resolution topology.

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Key concepts: Topology (electrical circuits), Space (punctuation), Product topology, General topology, Mathematics, Resolution (logic), Hilbert space, Weak topology (polar topology)