Shouldn't the topological space be $T_1$ for the Skyscraper sheaf to be a sheaf?

Question

Prove that the Skyscraper sheaf is a sheaf

A Skyscraper sheaf is defined in the following way:

Let $X$ be a topological space, with $p\in X$, and $S$ is a set. Let $i_p:p\to X$ be the inclusion. Then $i_{p,*}S(U)=S$ if $p\in U$, and $\{e\}$ if $p\notin U$

Shouldn't the space $X$ be $T_1$ for this to be a sheaf?