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Given a topological property $P$, we say that the space $X$ is $P$-generatedif for any subset $A\subset X$ that is not open in $X$ there is a subspace $Y\subset X$ with property $P$ such that $A\cap Y$ is not open in $Y$. (Ofcourse, in this definition we could replace "open" with "closed".)  In this paper we prove the following two results:  (1) Every Lindel\"of-generated regular space $X$ satisfying$|X|=\Delta(X)={\omega}_1$ is ${\omega}_1$-resolvable.  (2) Any (countable extent)-generated regular space $X$ satisfying$\Delta(X)>{\omega}$ is ${\omega}$-resolvable.  These are significant strengthenings of our earlier results from [JSSz] whichcan be obtained from (1) and (2) by simply omitting the "-generated" part.Moreover, the second result improves a recent result of Filatova and Osipovfrom [FO] which states that Lindel\"of-generated regular spaces of uncountabledispersion character are 2-resolvable.  [FO] Maria A. Filatova, Alexander V. Osipov On resolvability of Lindel\"ofgenerated spaces, arxiv:1712.00803. Siberian Electronic Mathematical Reports,Vol. 14, (2017) pp. 1444-1444.  [JSSz] Juh\'asz, Istv\'an; Soukup, Lajos; Szentmikl\'ossy, Zolt\'an, Regularspaces of small extent are ${\omega}$-resolvable. Fund. Math. 228 (2015), no.1, 27-46.

On the resolvability of Lindel\"of-generated and (countable extent)-generated spaces