Equihypocontinuity

Translation of "equihypocontinuity" into Russian

equihypocontinuity

Noun

equihypocontinuity

equihypocontinuities pl

эквигипоконтинуальность

The concept of equihypocontinuity is important in the study of functional analysis.

Понятие эквигипоконтинуальности важно в изучении функционального анализа.

Definitions

equihypocontinuity

Noun

(functional analysis) The property of a family of (typically multilinear) maps between topological vector spaces that, for every neighbourhood of zero in the codomain, there exist neighbourhoods of zero in each domain space such that the image of every map in the family, evaluated at any tuple from those neighbourhoods, lies in the given neighbourhood; equivalently, the controlling neighbourhoods can be chosen uniformly for the whole family.

To apply the theorem, one first proves the equihypocontinuity of the family of bilinear forms on the Fréchet space.

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Definitions