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Keywords:
maximally resolvable space; base at a point; $\pi$-base; $\pi$-character
maximally resolvable space; base at a point; $\pi$-base; $\pi$-character
Summary:
We compare several conditions sufficient for maximal resolvability of topo\-lo\-gi\-cal 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.
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