1999/10/27 by Gary Gruenhage, Gruenhage, Gary
Mathematics · #54D99 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54D99
paper · pdf · doi:10.48550/arxiv.math/9910153
16 pages, AMSTeX
arxiv created 1999/10/27 · arxiv updated 2009/11/30
We obtain several results and examples concerning the general question ``When must a space with a small diagonal have a Gdelta-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 Gdelta-diagonal; (3) every first-countable hereditarily Lindelof space with a small diagonal has a Gdelta-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 Gdelta diagonal.