On the closed subspaces of the inverse limit of finite dimensional vector spaces


Abstract in English

We prove that the sum A + B of closed subspaces A and B of the inverse limit of finite dimensional vector spaces, V = limVn (n ∈ N) over an algebraically closed field of characteristic 0 is closed. We extend also the basic fact that every ideal of a finite dimensional semisimple Lie algebra has a unique complement to the case of closed ideals of prosemisimple Lie algebras.

References used

Bourbaki, N. (1989), ''General Topology'', Chapters 1-4, Springer-Verlag
Hochschild, G. and Mostow, G. D. (1957), ''Representations and Representative functions of Lie Groups'', Ann. Of Math 66, 495-542
Humphreys, J. E. (1972), ''Introduction to Lie algebras and representation theory''. Second printing, Springer-Verlag

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