Polar topology

In functional analysis and related areas of mathematics a polar topology, topology of ${\displaystyle {\mathcal {A}}}$-convergence or topology of uniform convergence on the sets of ${\displaystyle {\mathcal {A}}}$ is a method to define locally convex topologies on the vector spaces of a dual pair.

Let ${\displaystyle (X,Y,\langle ,\rangle )}$ be a dual pair of vector spaces ${\displaystyle X}$ and ${\displaystyle Y}$ over the field ${\displaystyle \mathbb {F} }$, either the real or complex numbers.

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