Commit 2025-01-17 10:17 e5ab45ea
View on Github →feat: definition of linear topologies (#14990)
A topology on a module is linear if it is invariant by translation and if there
is a basis of neighborhoods consisting of submodules.
We are most interested in the case of rings: a topology on a ring is linear
if it is linear for both the left- and right-module structures on R over itself.
This is equivalent to being invariant by translation and admitting a
basis of neighborhoods consisting of two-sided ideals.
This will be used in a subsequent PR to evaluate multivariate power series.
We will also show that the natural topology on MvPowerSeries S R
is a linear topology when S
has a linear topology (e.g the discrete topology).