{"id":"palomar/PALOMAR-2026-10-19-000004","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/0bdc86b6daf37e26dae68c451ed9d811247f075d/topology/sigma-product-compactness","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000004-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54B10","msc:54D30","general-topology","sigma-products","compactness"],"score":0,"title":"Omega-bounded Sigma-products and a sharp compactness criterion","trust":"high","domain":"math.GN","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.GN","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true,"formalizes":[{"title":"On old and new classes of feebly compact spaces, arXiv:1804.07454v3","identifier":"https://arxiv.org/pdf/1804.07454v3","relationship":"formalizes"}]}