diff --git a/src/3_vector_spaces.md b/src/3_vector_spaces.md
index 803ccda500ba5d526875f796952e4d291e2d3804..8fffcf0ced93c70cb5e3f0fdaf6efab3dc0ea042 100644
--- a/src/3_vector_spaces.md
+++ b/src/3_vector_spaces.md
@@ -62,7 +62,7 @@ though the magnitude and direction of the vector itself remain unchanged.
     
 ## Properties of a vector space
 
-You might be familiar with the concept that one can perform a number of **operations** betweenvectors. Some important operations that are relevant in  this course are are:
+You might be familiar with the concept that one can perform a number of **operations** between vectors. Some important operations that are relevant in  this course are are:
 
 - **Addition**: I can add two vectors to produce a third vector, $\vec{a} + \vec{b}= \vec{c}$.
   As with scalar addition, also vectors satisfy the commutative property, $\vec{a} + \vec{b} = \vec{b} + \vec{a}$.
@@ -74,11 +74,9 @@ You might be familiar with the concept that one can perform a number of **operat
   Addition and scalar multiplication of vectors are both {\bf associative} and {\bf distributive}, so the following
   relations hold
   
-  1. $$(\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$
-  
-  2. $$\lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$
-
-  3. $$(\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$
+  - $$(\lambda \mu) \vec{a} = \lambda (\mu \vec{a}) = \mu (\lambda \vec{a})$$
+  - $$\lambda (\vec{a} + \vec{b}) = \lambda \vec{a} + \lambda \vec{b}$$
+  - $$(\lambda + \mu)\vec{a} = \lambda \vec{a} +\mu \vec{a}$$
 
 - **Vector product**: in addition to multiplying a vector by a scalar, as mentioned above, one can also multiply two vectors among them.
   There are two types of vector productions, one where the end result is a scalar (so just a number) and
@@ -109,10 +107,10 @@ The main properties of **vector spaces** are the following:
   to the same vector space
   
   $$\vec{a} \in {\mathcal V}, \qquad \vec{c} = \lambda \vec{a}
-  \in {\mathcal V}^n \qquad \forall\,\, \vec{a},\lambda$$
+  \in {\mathcal V}^n \qquad \forall\,\, \vec{a},\lambda \, .$$
 
-  The property that a vector space is complete upon scalar multiplication and vector addition is
-  also known as the **closure condition**.
+   The property that a vector space is complete upon scalar multiplication and vector addition is
+   also known as the **closure condition**.
 
   - There exists a **null element** $\vec{0}$ such that $\vec{a}+\vec{0} =\vec{0}+\vec{a}=\vec{a} $.