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Let $S$ be a numerical semigroup. We say that $h\in \mathbb{N}\setminus S$ is an isolated gap of $S$ if $\{h-1,h+1\}\subseteq S.$ A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by $\mathrm{m}\left(S\right)$ the multiplicity of a numerical semigroup $S$. A covariety is a nonempty family $𝒞$ of numerical semigroups that fulfills the following conditions: there exists the minimum of $𝒞,$ the intersection of two elements of $𝒞$ is again an element of $𝒞$, and $S\setminus \left\{\mathrm{m}\right(S\left)\right\}\in 𝒞$ for all $S\in 𝒞$ such that $S\ne min\left(𝒞\right).$ We prove that the set $𝒫\left(F\right)=\{S:S$ is a perfect numerical semigroup with...