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Cut-point spaces


Authors: B. Honari and Y. Bahrampour
Journal: Proc. Amer. Math. Soc. 127 (1999), 2797-2803
MSC (1991): Primary 54F15, 54F65
DOI: https://doi.org/10.1090/S0002-9939-99-04839-X
Published electronically: April 15, 1999
MathSciNet review: 1600152
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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.


References [Enhancements On Off] (What's this?)

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Additional Information

B. Honari
Affiliation: Faculty of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Email: honari@arg3.uk.ac.ir

Y. Bahrampour
Affiliation: Faculty of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Email: bahram@arg3.uk.ac.ir

DOI: https://doi.org/10.1090/S0002-9939-99-04839-X
Keywords: Continuum, cut-point space, cut point, non-cut point existence theorem, irreducible cut-point space, Khalimsky line
Received by editor(s): March 3, 1997
Received by editor(s) in revised form: November 20, 1997
Published electronically: April 15, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society

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