Weierstraß theorem: let be and then instead of so that

docs/theory/Optimality.md

@@ -24,8 +24,7 @@ We say that the problem has a solution if the budget set **is not empty**: $x^*
 
 ### Extreme value (Weierstrass) theorem
 
-Let $S \subset \mathbb{R}^n$ be a compact set and $f(x)$ a continuous function on $S$. 
-So that, the point of the global minimum of the function $f (x)$ on $S$ exists.
+Let $S \subset \mathbb{R}^n$ be a compact set, and let $f(x)$ be a continuous function on $S$. Then, the point of the global minimum of the function $f (x)$ on $S$ exists.
 :::
 
 ![A lot of practical problems are theoretically solvable](goodnews.png){#fig-weierstrass}
@@ -551,4 +550,4 @@ $$
 Optimization Problems with Inequality Constraints](https://www.scirp.org/pdf/OJOp_2013120315191950.pdf)
 * [On Second Order Optimality Conditions in
 Nonlinear Optimization](https://www.ime.usp.br/~ghaeser/secondorder.pdf)
-* [Numerical Optimization](https://www.math.uci.edu/~qnie/Publications/NumericalOptimization.pdf) by Jorge Nocedal and Stephen J. Wright. 
+* [Numerical Optimization](https://www.math.uci.edu/~qnie/Publications/NumericalOptimization.pdf) by Jorge Nocedal and Stephen J. Wright.