Resolvability in products of spaces of small cardinality

TL;DR

This paper proves that certain products of small-cardinality isodyne spaces are resolvable, extending known results to spaces of specific cardinalities and product sizes.

Contribution

It establishes new resolvability results for products of regular and Hausdorff isodyne spaces with particular small cardinalities.

Findings

Product of two regular isodyne spaces of size ω₁ is ω-resolvable

Product of n+2 Hausdorff isodyne spaces of size ωₙ is ω-resolvable

Extends resolvability results to spaces of specific small cardinalities

Abstract

We prove that: I. The product of any two regular isodyne spaces of cardinality $\omega_1$ is $\omega$-resolvable; II. The product of any $n + 2$ Hausdorff isodyne spaces of cardinality $\omega_n$ is $\omega$-resolvable.