2,223 reputation
523
bio website maths.lancs.ac.uk/~kania
location Lancaster, United Kingdom
age
visits member for 3 years, 11 months
seen 34 mins ago

21h
reviewed Approve What is a simplicial commutative ring from the point of view of homotopy theory?
Mar
18
comment Images of $\{0,1\}^\kappa$
Joseph, that cannot be right. Every subspace of $\{0,1\}^\kappa$ is zero-dimensional. As Bill says, every compact Hausdorff space is a continuous image of a zero-dimensional space and each zero-dimensional space $X$ embeds into $\{0,1\}^\kappa$ (for $\kappa$ equal to the weight of $X$). See Engelking's General topology.
Mar
18
revised Images of $\{0,1\}^\kappa$
added 44 characters in body
Mar
18
revised Images of $\{0,1\}^\kappa$
edited body
Mar
18
answered Images of $\{0,1\}^\kappa$
Mar
4
revised Communal problem books
a somewhat peculiar spelling corrected
Mar
1
revised Are countable unions of metrizable spaces metrizable too?
added 22 characters in body; edited title
Mar
1
comment The Banach space of bounded functions with countable support
arxiv.org/abs/1502.03026
Mar
1
comment What if Current Foundations of Mathematics are Inconsistent?
People were saying the same about the USSR.
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
will add that later
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 597 characters in body
Feb
26
comment Comparing cardinalities of the spectrum of two masas in $B(H)$
No, if $K$ satisfies the countable chain condition (and certainly the spectrum $K$ of $L_\infty(\mu)$ for a probability measure $\mu$ does), then no subspace of $C(K)$ is isomorphic to $c_0(\omega_1)$. (This is easy modulo certain prehistoric facts from Banach space theory.) I suggest deleting the old comments.
Feb
26
comment Comparing cardinalities of the spectrum of two masas in $B(H)$
No, in general you cannot embed $\beta \lambda$ into ${\rm spec}\, L_\infty(\{0,1\}^{\lambda})$. This fails for all uncountable $\lambda$. (You will find this in old papers of H. P. Rosenthal.)
Feb
26
comment Comparing cardinalities of the spectrum of two masas in $B(H)$
@Manny Reyes, for non-separable spaces the situation is trickier but I guess that the only types of masas are the following: $\ell_\infty(\lambda)$ and $L_\infty(\{0,1\}^\lambda)$ and certain $\ell_\infty$-sums of them ($\lambda$ is the dimension of the Hilbert space) but at the end of the day the spectra will have the same cardinality.
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 27 characters in body
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 130 characters in body
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 130 characters in body
Feb
26
revised Comparing cardinalities of the spectrum of two masas in $B(H)$
added 194 characters in body
Feb
26
answered Comparing cardinalities of the spectrum of two masas in $B(H)$
Feb
22
comment Totally disconnected subspaces
The double arrow space (aka the split interval) is the canonical example.