Resolvability of spaces having small spread or extent
István Juhász, Lajos Soukup and Zoltán Szentmiklóssy
In a recent paper O. Pavlov proved the following two interesting
resolvability results:
 If a space satisfies
then
is maximally resolvable.
 If a space satisfies
then
is resolvable.
Here
(
) denotes the smallest successor
cardinal such that has no discrete (closed discrete) subset of
that size and is the smallest cardinality of a nonempty
open set in . In this note we improve (1) by showing that
can be relaxed to
. In particular,
if is a space of countable spread with
then
is maximally resolvable.
The question if an analogous improvement of (2) is valid remains
open, but we present a proof of (2) that is simpler than Pavlov's.

 1

O. Pavlov, On resolvability of topological spaces
Topology and its Applications 126 (2002) 3747.
2000 Mathematics Subject Classification: 54A25, 54B05
Key words and phrases: resolvable space, maximally resolvable space,
dispersion character, spread, extent
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