Topology on diffeological vector spaces
Enxin Wu, Zhongqiang Yang

TL;DR
This paper investigates the conditions under which the D-topology renders diffeological vector spaces into topological vector spaces, identifying cases where this holds and proposing the study of almost topological vector spaces.
Contribution
It demonstrates that the D-topology makes many diffeological vector spaces into topological vector spaces using $k_$-space theory, but not universally, and introduces the concept of almost topological vector spaces.
Findings
D-topology induces topological vector space structure for a large class of diffeological vector spaces.
Counterexamples show that this is not true for all diffeological vector spaces.
Proposes the study of almost topological vector spaces as a new class.
Abstract
It is expected that the -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 -space theory, but not so in general. The paper also proposes the study of a class of almost topological vector spaces.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Topology and Set Theory · Fixed Point Theorems Analysis
