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:

1. If a space satisfies then is maximally resolvable.
2. 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 non-empty 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.

Bibliography

1
O. Pavlov, On resolvability of topological spaces Topology and its Applications 126 (2002) 37-47.

2000 Mathematics Subject Classification: 54A25, 54B05

Key words and phrases: -resolvable space, maximally resolvable space, dispersion character, spread, extent