Topology on diffeological vector spaces

Enxin Wu, Zhongqiang Yang

Published 2022-05-19Version 1

It is expected that the $D$-topology makes every diffeological vector space into a topological vector space. We show that it is the case for a large class of diffeological vector spaces via $k_\omega$-space theory, but not so in general. The paper also proposes the study of a class of almost topological vector spaces.