Timeline for Fundamental group of Lie groups
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2010 at 19:15 | comment | added | Andreas Blass | You don't need to assume a common identity element; it suffices to assume that each operation has its own 2-sided identity. (Of course, it ultimately follows that the two identity elements are equal.) Also, the hypothesis in the E-H argument, that each of the operations is a homomorphism with respect to the other, is not what is usually called distributivity. (For example, the meet and join operations in a distributive lattice are each distributive over the other, but this mutual distributivity is not what is wanted for the E-H argument.) | |
| Aug 20, 2010 at 15:38 | comment | added | Robert Bruner | I've always found it entertaining that one proves commutativity before associativity in this argument. | |
| Aug 20, 2010 at 7:11 | comment | added | Andrew Stacey | The link in my answer is to the nLab page where an even weaker hypothesis is assumed: "If a set is equipped with two binary operations with identity elements, as long as they commute with each other in the sense that one is (with respect to the other) a homomorphism of sets with binary operations, then everything else follows.". The argument is, as you say, quite formal and works in extremely general cases. | |
| Aug 19, 2010 at 22:42 | comment | added | Sean Tilson | i believe this is exactly what Andrew mentioned above... minus that reference | |
| Aug 19, 2010 at 2:59 | history | answered | Hannay | CC BY-SA 2.5 |