1. CMB 2011 (vol 56 pp. 203)
|Productively LindelÃ¶f Spaces May All Be $D$|
We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every LindelÃ¶f space is LindelÃ¶f, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.
Keywords:productively LindelÃ¶f, $D$-space, projectively $\sigma$-compact, Menger, Hurewicz
Categories:54D20, 54B10, 54D55, 54A20, 03F50
2. CMB 2010 (vol 54 pp. 270)
|Sequential Order Under PFA|
It is shown that it follows from PFA that there is no compact scattered space of height greater than $\omega$ in which the sequential order and the scattering heights coincide.
Keywords:sequential order, scattered spaces, PFA
Categories:54D55, 03E05, 03E35, 54A20