A FINITE DIMENSIONAL HOMOGENEOUS CLAN IS A GROUP

@article{Hudson1963AFD,
  title={A FINITE DIMENSIONAL HOMOGENEOUS CLAN IS A GROUP},
  author={A. L. Hudson and P. Mostert},
  journal={Annals of Mathematics},
  year={1963},
  volume={78},
  pages={41}
}
A clan is a compact connected semigroup with identity. The purpose of this paper is to give a proof of the title. This gives an affirmative answer to the question of Wallace [9], and supplies the weakest algebraic conditions now extant for obtaining the compact connected (finite dimensional) groups. A space X is homogeneous if for any two points x, y E X, there is a homeomorphism qp of X onto itself such that (p(x) = y. Insofar as this result is concerned, covering, inductive, or cohomological… Expand
12 Citations
(L)-Semigroup Sums
  • J. Martin
  • Mathematics, Computer Science
  • Axioms
  • 2019
  • 14
  • PDF
CLANS ON GROUP-SUPPORTING SPACES1
  • PDF
Semigroups with identity on Peano continua.
  • 1
  • PDF
...
1
2
...

References

SHOWING 1-6 OF 6 REFERENCES
Totally ordered commutative semigroups
  • 49
  • Highly Influential
  • PDF
A cohomological definition of dimension for locally compact Hausdorff spaces
  • 74
  • Highly Influential
Arcs in partially ordered spaces.
  • 47
  • PDF
Topological Transformation Groups
  • 927
One-dimensional homogeneous clans are groups
  • 5