Following Malykhin, we say that a space $X$ is extraresolvable if $X$ contains a family $𝒟$ of dense subsets such that $\left|𝒟\right|>\Delta \left(X\right)$ and the intersection of every two elements of $𝒟$ is nowhere dense, where $\Delta \left(X\right)=min\left\{\right|U|:U$ is a nonempty open subset of $X\}$ is the dispersion character of $X$. We show that, for every cardinal $\kappa$, there is a compact extraresolvable space of size and dispersion character $2^{\kappa }$. In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) $2^{\kappa }<2^{{\kappa }^{+}}$, 2) ${\left({\kappa }^{+}\right)}^{\kappa }$ is extraresolvable and...