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F{K} spaces, their duals and the visualisation of neighbourhoods. (English) Zbl 1102.68679

Summary: We demonstrate how our software package for visualisation and animations in mathematics can be applied to the representation of neighbourhoods and weak neighbourhoods in certain topologies that arise in the theory of \(FK\) spaces and matrix transformations. We also prove some new results that reduce the determination of the \(\beta\)-duals of matrix domains \(X_\Delta\) of the difference operator \(\Delta\) in \(FK\) spaces \(X\) with \(AK\) to that of the \(\beta\)-dual of \(X\) itself.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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