split(topology/algebra/infinite_sum): Split into four files (#18414)

Over the past five years, `topology.algebra.infinite_sum` has grown pretty big. This PR splits off a third of it to three new files. Precisely, split `topology.algebra.infinite_sum` into:
* `topology.algebra.infinite_sum.basic`: Definitions and theory in monoids. All this will be multiplicativised in #18405.
* `topology.algebra.infinite_sum.ring`: Interaction of infinite sums and (scalar) multiplication. This mostly cannot be multiplicativised.
* `topology.algebra.infinite_sum.order`: Interaction of infinite sums and order. Most of this will be multiplicativised in #18405.

Incidentally, this brings down some files' imports by quite a lot.

Also move the `star` and `mul_opposite` material to the end of the file to facilitate multiplicativisation in #18405.

Johannes wrote some of all these files, except `topology.algebra.infinite_sum.real` whose first lemma I could trace back as coming from #753, with the others coming from #1739.

src/analysis/analytic/basic.lean

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel, Yury Kudryashov
 import analysis.calculus.formal_multilinear_series
 import analysis.specific_limits.normed
 import logic.equiv.fin
-import topology.algebra.module.infinite_sum
+import topology.algebra.infinite_sum.module
 
 /-!
 # Analytic functions

src/analysis/analytic/isolated_zeros.lean

@@ -7,7 +7,6 @@ import analysis.analytic.basic
 import analysis.calculus.dslope
 import analysis.calculus.fderiv_analytic
 import analysis.calculus.formal_multilinear_series
-import topology.algebra.infinite_sum
 import analysis.analytic.uniqueness
 
 /-!

src/analysis/complex/basic.lean

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel
 import data.complex.module
 import data.complex.exponential
 import data.is_R_or_C.basic
-import topology.algebra.module.infinite_sum
+import topology.algebra.infinite_sum.module
 import topology.instances.real_vector_space
 
 /-!

src/analysis/normed_space/finite_dimension.lean

@@ -10,7 +10,7 @@ import analysis.normed_space.operator_norm
 import analysis.normed_space.riesz_lemma
 import linear_algebra.matrix.to_lin
 import topology.algebra.module.finite_dimension
-import topology.algebra.module.infinite_sum
+import topology.algebra.infinite_sum.module
 import topology.instances.matrix
 
 /-!

src/measure_theory/measure/outer_measure.lean

@@ -7,7 +7,6 @@ import analysis.specific_limits.basic
 import measure_theory.pi_system
 import data.countable.basic
 import data.fin.vec_notation
-import topology.algebra.infinite_sum
 
 /-!
 # Outer Measures

src/number_theory/l_series.lean

@@ -6,7 +6,7 @@ Authors: Aaron Anderson
 import analysis.normed_space.finite_dimension
 import analysis.p_series
 import number_theory.arithmetic_function
-import topology.algebra.infinite_sum
+import topology.algebra.infinite_sum.basic
 
 /-!
 # L-series