S EPARABLE S PACES
K ILLING
K ILLING S-S PACES AND G ETTING AWAY
W ITH I T
W EAKENINGS OF ♦ AND STRONG SEPARABILITY
Erik A. Andrejko
University of Wisconsin - Madison
Mar 25 2008
E RIK A. A NDREJKO K ILLING S-S PACES AND G ETTING AWAY W ITH I T

S EPARABLE S PACES
K ILLING
S PACES
D EFINITION
A space X is called separable if it contains a countable dense subset.
D EFINITION
A space X is called right separated if it contains an uncountable
subspace {xξ : ξ < ω1 } in which for each η < ω1
{xξ : ξ < η} is open
E RIK A. A NDREJKO K ILLING S-S PACES AND G ETTING AWAY W ITH I T

S EPARABLE S PACES
K ILLI