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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1600152