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Some topological properties of almost $P$-spaces are studied in
[4],[9], [12] and [15]. In this paper, we give some algebraic
characterizations of these spaces. Also, we obtain some more
properties for these spaces. It is shown that the one-point
compactification of a locally compact space $X$ is an almost
$P$-space if and only if $X$ is a non-Lindel$\ddot{\text{o}}$f
almost $P$-space. Using this, we reduce some problems concerning
compact almost $P$-spaces to locally compact ones. It is shown
that a locally compact almost $P$-space of cardinality less than
$2^{\aleph_1}$ has an uncountable dense set of isolated points.
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