Motivation for the question:
In our current lecture we use the term 'trace topology' instead of 'subspace topology'
Since I tend to try to understand such terminology, origin and applications to understand the big picture a bit more, I was searching for the origin of the term.
And I honestly didn't found a good explanation for it at all.
Every source always directly mentions it as a 'subspace topology' and mostly ignores the term 'trace topology' and if it is used, the origin is never explained, it's always viewed as a 'subspace topology'.
Where does the term 'trace topology' originated from and what role does the term 'trace' fulfil.