Timeline for On the compactness of a certain chain topology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2012 at 7:59 | comment | added | Joel David Hamkins | I have seen them used several times, but only as counterexamples, since a space in which the open sets are linearly ordered by inclusion are unusual in several respects. I am sorry that I don't have any specific reference. | |
| Jun 19, 2012 at 7:48 | vote | accept | K A Khan | ||
| Jun 19, 2012 at 7:48 | comment | added | K A Khan | @ Joel thanx for the answer.can you tell me the areas of topology where such chains could be found? any research paper? Any particular name that could be given to such a topology? | |
| Jun 16, 2012 at 17:35 | comment | added | Joel David Hamkins | If you don't assume that $I$ is a topology, then it is not correct to say that the topology generated by $I$ is compact if and only if $I$ has a largest proper subset of $X$, since perhaps the proper subsets of $X$ in $I$ union up to something strictly smaller than $X$, but this set does not appear in $I$. In this case, the topology would still be compact, but there wouldn't be a largest proper subset in $I$ (although there would be a largest proper subset in the generated topology). | |
| Jun 16, 2012 at 14:20 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |