© | Dror Bar-Natan: Classes: 2010-11: 327/Topology:

Video Topology-100927

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Videography by Qian (Sindy) Li

Notes on Topology-100927:    [edit, refresh]

Managed by dbnvp: Tip: blackboard shots are taken when the discussion of their content has just ended. To see the beginning of the discussion on a certain blackboard, roll the video to the time of the preceeding blackboard.

0:00:00 [edit] What a sad first frame...
0:04:16 [edit] Review of basis for finite product spaces
0:05:04 [edit] We review the characterization of subspace topology and the definition of subspace topology
0:05:51 [edit] definition of a closed set
0:06:07 [edit] We want to show some nontrivial clopen sets in some topological spaces.
0:07:22 [edit] An example of a nontrivial clopen set in the topological space of all the rational numbers as a subspace of Rstd
0:11:12 [edit] definition of cantor set
0:15:17 [edit] proof of cantor set is closed
0:18:43 [edit] definition of the lebesgue measure(length) of the cantor set
0:22:30 [edit] another equivalent definition of the cantor set
0:23:52 [edit] Why the cantor set is uncountable
0:32:43 [edit] definition of the closure of a set A in a topological space X
0:35:44 [edit] the interior of a set A in a topological space X
0:39:11 [edit] characterization of closure of A in a topological space X. the set of all elements in X that every open nbd of the element intersects A.