Cut-point spaces

Honari, B.; Bahrampour, Y.

doi:10.1090/S0002-9939-99-04839-X

Cut-point spaces
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by B. Honari and Y. Bahrampour PDF

Proc. Amer. Math. Soc. 127 (1999), 2797-2803 Request permission

Abstract:

The notion of a cut-point space is introduced as a connected topological space without any non-cut point. It is shown that a cut-point space is infinite. The non-cut point existence theorem is proved for general (not necessarily $T_1$) topological spaces to show that a cut-point space is non-compact. Also, the class of irreducible cut-point spaces is studied and it is shown that this class (up to homeomorphism) has exactly one member: the Khalimsky line.

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