K-space (functional analysis)

In mathematics, more specifically in functional analysis, a K-space is an F-space ${\displaystyle V}$ such that every extension of F-spaces (or twisted sum) of the form $${\displaystyle 0\rightarrow \mathbb {R} \rightarrow X\rightarrow V\rightarrow 0.\,\!}$$ is equivalent to the trivial one^[1] $${\displaystyle 0\rightarrow \mathbb {R} \rightarrow \mathbb {R} \times V\rightarrow V\rightarrow 0.\,\!}$$ where ${\displaystyle \mathbb {R} }$ is the real line.