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Jan 2, 2012 at 15:47 comment added Gerald Edgar OK, you explained it. To me, $2^{\omega_1}$ is a certain calculation in ordinal arithmetic... For your example, I would say: a set of power $\aleph_1$ with discrete topology. That way, I even avoid confusing ordinals with cardinals.
Jan 2, 2012 at 10:56 comment added user5810 The discrete topology (which is why the second entry in the ordered pair is the set of all subsets of $\omega_1$).
Jan 2, 2012 at 10:52 comment added Paul What's the topology on $X$?
Jan 2, 2012 at 10:34 history answered user5810 CC BY-SA 3.0