Timeline for Scott topology, but for graphs
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 13, 2011 at 12:32 | comment | added | Ben Sprott | This comment is coming far too late, but I had a look at the Borel-reducibility notion and I think it is quite interesting. I might have been thinking about functors in terms of Borel reducibility. For instance, an equivalence relation in category theory is over morphisms like $fg=h$ A functor maps diagrams to diagrams, so $F: fg=h \rightarrow F(f)F(g)=F(h)$ I was trying to see functors as equivalence relations going into more or less "simple" (a term used to compare Borel Relations) equivalence relations. Joel's post is actually insightful as to my thinking. Thanks Joel. | |
| Jun 25, 2011 at 19:47 | comment | added | Ben Sprott | Hi, Yes, I was thinking of the basic relationship between dcpos and directed graphs where an edge is interpreted as the relation in the dcpo. So, the Scott continuous map is defined on an individual dcpo and its language contains reference mainly to the ordering relation. Thus, a similarly defined continuous map for a graph would concern edges. | |
| Jun 25, 2011 at 12:59 | comment | added | Joel David Hamkins | This answer describes a commonly used natural topology on the space of all graphs, rather than a topology on a fixed graph, and I realize now that perhaps this isn't what was desired. | |
| Jun 25, 2011 at 12:52 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |