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COMPACT SPACES OF THE FIRST BAIRE CLASS THAT HAVE OPEN FINITE DEGREE
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 17 / Issue 5 / November 2018
- Published online by Cambridge University Press:
- 21 November 2016, pp. 1173-1196
- Print publication:
- November 2018
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We introduce the open degree of a compact space, and we show that for every natural number
$n$, the separable Rosenthal compact spaces of degree 
$n$ have a finite basis.
Productively Lindelöf Spaces May All Be D
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- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 1 / 01 March 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 203-212
- Print publication:
- 01 March 2013
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We give easy proofs that (a) the Continuum Hypothesis implies that if the product of
$X$ with every Lindelöf space is Lindelöf, then $X$ is a 
$D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz.
Sequential Order under PFA
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- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 2 / 01 June 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 270-276
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- 01 June 2011
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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.
Natural Covers and R-Quotient Maps
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- Journal:
- Canadian Mathematical Bulletin / Volume 25 / Issue 4 / 01 December 1982
- Published online by Cambridge University Press:
- 20 November 2018, pp. 456-461
- Print publication:
- 01 December 1982
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