Open Research Index

Omega-bounded Sigma-products and a sharp compactness criterion

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-19-000004Oct 19, 2026math.GNscore 0

For arbitrary T1 omega-bounded factors with an explicit product basepoint, the countable-support Sigma-product is omega-bounded and countably compact. Every countable family is trapped, together with its ambient closure, in a closed compact coordinate box using one countable support. For compact Hausdorff factors, the Sigma-product is compact if and only if only countably many factors contain a point different from the basepoint. Uncountable discrete Boolean Sigma-products are countably compact but not compact. The index and factor universes are independent; the empty index and empty…

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