Talk:Partition topology
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Check the usage of the separation axioms from COT are the same as those on wikipedia. jbolden1517Talk 01:10, 12 June 2006 (UTC)
Sure about the odd-even topology? We have:
but I wonder whether it ought to be:
As it stands, there is no indication that k needs to be the same for both the 2k and 2k+1 sets.
In fact, Steen and Seebach have it as:
which emphasises and clarifies the specific range of k. It ultimately comes to the same thing, of course, but it allays the confusion over whether the conventional understanding of includes zero or not. --Matt Westwood 22:55, 28 May 2011 (UTC)
Each point of X is a set in P?
[edit]The article says:
"The trivial partitions yield the discrete topology (each point of X is a set in P) or indiscrete topology (P = {X})."
What if the space is X=R^2 (it is not a space of sets, but of points), each point of X can't be a set in P, because it's elements are not sets.
This should be clarified. — Preceding unsigned comment added by 186.18.76.220 (talk) 20:46, 28 October 2011 (UTC)
- Yes it can - each element of X is an ordered pair. So each set of the discrete topology contains a set of ordered pairs of X = R^2. — Preceding unsigned comment added by WestwoodMatt (talk • contribs) 23:03, 28 October 2011 (UTC)