On the Non-Cutpoint Existence Theorem
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 213-216
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The theorem of the title asserts that every non-degenerate continuum (that is, every compact connected Hausdorff space containing more than one point) contains at least two non-cutpoints. This is a fundamental result in set - theoretic topology and several standard proofs, each varying from the others to some extent, have been published. (See, for example, [1], [4] and [5]). The author has presented a less standard proof in [3] where the non-cutpoint existence theorem was obtained as a corollary to a result on partially ordered spaces. In this note a refinement of that argument is offered which seems to the author to be the simplest proof extant. To facilitate its exposition, the notion of a weak partially ordered space is introduced and the cutpoint partial order of connected spaces is reviewed.
Ward, L. E. On the Non-Cutpoint Existence Theorem. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 213-216. doi: 10.4153/CMB-1968-024-2
@article{10_4153_CMB_1968_024_2,
author = {Ward, L. E.},
title = {On the {Non-Cutpoint} {Existence} {Theorem}},
journal = {Canadian mathematical bulletin},
pages = {213--216},
year = {1968},
volume = {11},
number = {2},
doi = {10.4153/CMB-1968-024-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-024-2/}
}
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