# Thompson's construction, The empty-expression

Why this case exists in Thompson's construction algorithm?

Isn't just a special case of:

where the symbol a is replaced by ϵ?

It's not a special case since $a$ is a symbol of the alphabet whereas $\epsilon$ is a symbol representing the empty word. However, you could lump the two cases together if you wish.
It all boils down to your recursive definition of regular expression. Most definitions will have three "axioms": $a$ for $a \in \Sigma$, $\epsilon$, and $\emptyset$. This necessitates three different base cases in the construction.