Topological property of DNA
DNA supercoiling can be described numerically by changes in the linking number $L_k$, it's the most descriptive property of supercoiled DNA.

The linking number $L_k$ is equivalent to the sum of $Tw$, which is the number of twists or turns of the double helix, and $Wr$ which is the number of coils or writhes.

$$L_k = Tw + Wr$$


  [...]  If there is a closed DNA molecule, the sum of $Tw$ and $Wr$, or the linking number, does not change. [...] Since the linking number L of supercoiled DNA is the number of times the two strands are intertwined (and both strands remain covalently intact), L cannot change. 


I don't know how to explain it more but I think the main idea is represented in the image below.



Edit:

From DNA Topology: Fundamentals :

There are two important features of the $L_k$:


$L_k$ is always an integer.
$L_k$ cannot be changed by any deformation of the DNA strands, i.e. it is topologically invariant. The only way to change it is to introduce a break in one or both DNA strands, rotate the two DNA strands relative to each other and seal the break. This is precisely the role of DNA
topoisomerases.


Related question: Reason behind formation of positive supercoils during DNA replication/transcription.

Sources : DNA supercoil and DNA Topology.