Сходимость и секвенциальная сходимость в некоторых функциональных топологических векторных пространствах

S. S. Platonov

Petrozavodsk State University, Faculty of Mathematics

Abstract: In some function spaces, which are inductive limits of the normed spaces, the connections between various definitions of convergence of sequences, boundednes and closure of sets are investigated. In particular, the spaces consisting of functions on homogeneous spaces of locally compact topological groups are considered. The equivalence to a closure and sequential closure for linear $G$-invariant subspaces is proved.

UDC: 517

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