diff --git a/semialgebraic_universal_covers_v2.txt b/semialgebraic_universal_covers_v2.txt
index 4b3bbd6..278bf3c 100644
--- a/semialgebraic_universal_covers_v2.txt
+++ b/semialgebraic_universal_covers_v2.txt
@@ -348,10 +348,10 @@ subspace. The Stein condition holds only at the boundary, locally.
 -----------------------------------------------------
 
 Before diving into the boundary analysis, we handle the base case:
-what if the boundary Y \ V has empty interior at the level of real
+what if the boundary Y  V has empty interior at the level of real
 hypersurfaces? This is the inductive anchor.
 
-Let L := Y \ V = the boundary. Let n = dim_C Y = dim_R / 2.
+Let L := Y  V = the boundary. Let n = dim_C Y = dim_R / 2.
 
 Claim. If L contains no real analytic hypersurface patch (no real
 2n-1 dimensional regular real algebraic submanifold) then V is a
@@ -369,15 +369,15 @@ at most 2n - 2.
 Step 3. Now apply Theorem (Vajaitu 2000, Theorem 1) to L. Statement:
 let M be a complex manifold of complex dimension n, and let A be a
 closed subanalytic subset of M of real dimension at most 2n - 2.
-If M \ A is locally pseudoconvex at A, then A is a complex analytic
+If M  A is locally pseudoconvex at A, then A is a complex analytic
 subset of M of pure dimension n - 1 (or A is empty).
 
-Here M = Y, A = L, and M \ A = V is locally pseudoconvex by 3.2.
+Here M = Y, A = L, and M  A = V is locally pseudoconvex by 3.2.
 Conclusion: L is complex analytic of pure dimension n - 1.
 
 Step 4. Complex analytic subsets of projective varieties are
 algebraic (Chow's theorem, Serre 1956). So L is algebraic, hence V
-= Y \ L is a Zariski open subset of Y, hence automatically
+= Y  L is a Zariski open subset of Y, hence automatically
 semialgebraic and open.
 
 QED.
@@ -407,7 +407,7 @@ the bulk of V near a boundary face as an "epigraph" over P. This
 tower will turn out to be exactly the contractible Stein base M in the
 eventual intrinsic quotient f_X : X~ -> M.
 
-If the boundary L = Y \ V has no real hypersurface patch (Section
+If the boundary L = Y  V has no real hypersurface patch (Section
 3.3), then P is a point and we are done with this step. Otherwise
 run a dimension-decreasing recursion.
 
@@ -918,7 +918,7 @@ inside L along which E degenerates). Enlarge the fibre E_y slightly
 at a regular wall point y_0 in W. By (a), the fibre E_y for y -> y_0
 from a generic side is exactly the epigraph of the paraboloid over
 H(y). Take the one-sided limit as y -> y_0 through the generic side.
-Because H(y_0, v_\perp) is analytic (in v_\perp, the transverse wall
+Because H(y_0, v_perp) is analytic (in v_perp, the transverse wall
 variable), the limit epigraph is exactly the paraboloid over H(y_0).
 So E_{y_0} contains the paraboloid over H(y_0). Going back through
 the wall to the other side: by the same argument on the other side,
@@ -944,10 +944,10 @@ theorem (holes:thin-analyticity, Section 3.2 preliminaries;
 Vajaitu 2000, Theorem 1):
 
   If A is a closed subanalytic subset of real dimension <= 2 ell - 2,
-  and if M \ A is locally pseudoconvex, then A is complex analytic.
+  and if M  A is locally pseudoconvex, then A is complex analytic.
 
 Here M corresponds to a small ball inside V_2 near y_0 (a thin set),
-A corresponds to S_sing, and M \ A is the open piece of V_2 on which
+A corresponds to S_sing, and M  A is the open piece of V_2 on which
 E_y = epigraph. Conclusion: S_sing is complex analytic in V_2, so it
 is closed analytic. But V_2 is itself semialgebraic open, and complex
 analytic subsets of projective varieties are algebraic (Chow, Serre
@@ -1997,7 +1997,7 @@ The compactifiable-cover lemma.
   proper modification that is an isomorphism over a^{-1}(N^0))
   and h : U_hat -> C such that h|_{U} = c o r^{-1} o a.
 
-  Put U_hat_U := tau^{-1}(U). The complement U_hat \ U_hat_U is an
+  Put U_hat_U := tau^{-1}(U). The complement U_hat  U_hat_U is an
   analytic subset of the compact smooth projective manifold U_hat.
   Apply the Campana core plus SpecialAbelianity (3.7.1's citation):
   the deck group of the covering U -> N is virtually abelian.
@@ -2238,7 +2238,7 @@ Application.
   So A = T by cmp:closed-rigidity: P_{x_0} is dense in T.
 
   - Since P_{x_0} is semialgebraic and dense, and T is connected,
-    P_{x_0} = T (semialgebraicity: if T \ P_{x_0} were nonempty
+    P_{x_0} = T (semialgebraicity: if T  P_{x_0} were nonempty
     open, then P_{x_0} could not be dense).
 
 Conclusion. All fibres are polarized-isomorphic to F := F_{x_0}.