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On a class of semigroups on $E\sb n$
1956
Proceedings of the American Mathematical Society
Euclidean space), and with other restrictions. Here, we classify all (topological) semigroups on the half line [0, ) in which 0 and 1 play their natural roles of zero and identity, and use this as an aid in classifying semigroups 5 with identity on En, «>1, such that some (« -1)-dimensional compact connected submanifold is a subsemigroup containing the identity of 5. It turns out that only E2 and £4 will admit such a situation. In fact, we prove the following two theorems (see §1 for
doi:10.1090/s0002-9939-1956-0078646-6
fatcat:3cpnk3ebuvbd7p7yho62ttu5aa