Spaces having a small diagonal

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dc.creatorGruenhage, Gary
dc.date1999-10-27
dc.date.accessioned2026-07-07T05:31:19Z
dc.date.available2026-07-07T05:31:19Z
dc.descriptionWe obtain several results and examples concerning the general question ``When must a space with a small diagonal have a G_delta-diagonal?". In particular, we show (1) every compact metrizably fibered space with a small diagonal is metrizable; (2) there are consistent examples of regular Lindelof (even hereditarily Lindelof) spaces with a small diagonal but no G_delta-diagonal; (3) every first-countable hereditarily Lindelof space with a small diagonal has a G_delta-diagonal; (4) assuming CH, every Lindelof Sigma-space with a small diagonal has a countable network; (5) whether countably compact spaces with a small diagonal are metrizable depends on your set theory; (6) there is a locally compact space with a small diagonal but no G_delta diagonal.
dc.description16 pages, AMSTeX
dc.identifierhttps://arxiv.org/abs/math/9910153
dc.identifierhttp://arxiv.org/abs/math/9910153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79296
dc.subjectGeneral Topology
dc.subject54D99
dc.titleSpaces having a small diagonal
dc.typetext

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