bio  website  maths.lancs.ac.uk/~kania 

location  Lancaster, United Kingdom  
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21h

reviewed  Approve What is a simplicial commutative ring from the point of view of homotopy theory? 
Mar 18 
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Images of $\{0,1\}^\kappa$
Joseph, that cannot be right. Every subspace of $\{0,1\}^\kappa$ is zerodimensional. As Bill says, every compact Hausdorff space is a continuous image of a zerodimensional space and each zerodimensional space $X$ embeds into $\{0,1\}^\kappa$ (for $\kappa$ equal to the weight of $X$). See Engelking's General topology. 
Mar 18 
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Images of $\{0,1\}^\kappa$
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Mar 18 
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Images of $\{0,1\}^\kappa$
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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?
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Mar 1 
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The Banach space of bounded functions with countable support
arxiv.org/abs/1502.03026 
Mar 1 
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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 
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Comparing cardinalities of the spectrum of two masas in $B(H)$
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Feb 26 
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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 
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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 
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Comparing cardinalities of the spectrum of two masas in $B(H)$
@Manny Reyes, for nonseparable 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 
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Comparing cardinalities of the spectrum of two masas in $B(H)$
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Feb 26 
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Comparing cardinalities of the spectrum of two masas in $B(H)$
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Feb 26 
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Feb 26 
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Comparing cardinalities of the spectrum of two masas in $B(H)$
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Feb 26 
answered  Comparing cardinalities of the spectrum of two masas in $B(H)$ 
Feb 22 
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Totally disconnected subspaces
The double arrow space (aka the split interval) is the canonical example. 