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October 3, 2025Open Access

R^ω₁-Factorizable Spaces and Groups

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This study demonstrates that a Tychonoff space is Rω1-factorizable if bounded by specific conditions, highlighting implications in topology.

A Tychonoff space is Rω1-factorizable if the product with a discrete space is z-embedded in its compactification.
Rω1-factorizable spaces are hereditarily Lindelöf and hereditarily separable, indicating properties of space structure.
The independence of nonmetrizable Rω1-factorizable spaces from ZFC illustrates rich complexities in topology.
Under CH, all Rω1-factorizable spaces are second-countable; under MA + ¬CH, certain structures remain Rω1-factorizable.

Lipin et al. (2025) studied this question.

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This study demonstrates that a Tychonoff space is Rω1-factorizable if bounded by specific conditions, highlighting implications in topology.