Abstract:We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space $X$ is maximally resolvable provided that for a dense set $X_0\subset X$ and for each $x\in X_0$ the $\pi $-character of $X$ at $x$ is not greater than the dispersion character of $X$. On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.
Keywords: maximally resolvable space, base at a point, $\pi $-base, $\pi $-character
AMS Subject Classification: 54A10, 54A25