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1. CMB Online first
On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces We establish that if it is consistent that there is a
supercompact cardinal, then it is consistent that every locally
compact, hereditarily normal space which does not include a perfect
pre-image of $\omega_1$ is hereditarily paracompact.
Keywords:locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$ Categories:54D35, 54D15, 54D20, 54D45, 03E65, 03E35 |
2. CMB 2010 (vol 53 pp. 360)
Separating H-sets by Open Sets In an H-closed, Urysohn space, disjoint H-sets can be separated by disjoint open sets. This is not true for an arbitrary H-closed space even if one of the H-sets is a point. In this paper, we provide a systematic study of those spaces in which disjoint H-sets can be separated by disjoint open sets.
Keywords:H-set, H-closed, θ-continuous Categories:54C08, 54D10, 54D15 |
3. CMB 2005 (vol 48 pp. 195)
On Suslinian Continua A continuum is said to be Suslinian if it does not contain uncountably
many mutually exclusive nondegenerate subcontinua. We prove that
Suslinian continua are perfectly normal and rim-metrizable. Locally
connected Suslinian continua have weight at most $\omega_1$ and under
appropriate set-theoretic conditions are metrizable. Non-separable
locally connected Suslinian continua are rim-finite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rim-metrizable,, perfectly normal, rim-finite Categories:54F15, 54D15, 54F50 |
4. CMB 1998 (vol 41 pp. 245)
The normality in products with a countably compact factor It is known that the product $\omega_1 \times X$ of
$\omega_1$ with an $M_1$-space may be nonnormal. In this paper we
prove that the product $\kappa \times X$ of an uncountable regular
cardinal $\kappa$ with a paracompact semi-stratifiable space is normal
if{f} it is countably paracompact. We also give a sufficient
condition under which the product of a normal space with a paracompact
space is normal, from which many theorems involving such a product
with a countably compact factor can be derived.
Categories:54B19, 54D15, 54D20 |