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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Local finite cohesion


Author: W. C. Chewning
Journal: Trans. Amer. Math. Soc. 176 (1973), 385-400
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9947-1973-0355998-5
MathSciNet review: 0355998
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Abstract: Local finite cohesion is a new condition which provides a general topological setting for some useful theorems. Moreover, many spaces, such as the product of any two nondegenerate generalized Peano continua, have the local finite cohesion property. If X is a locally finitely cohesive, locally compact metric space, then the complement in X of a totally disconnected set has connected quasicomponents; connectivity maps from X into a regular $ {T_1}$ space are peripherally continuous; and each connectivity retract of X is locally connected. Local finite cohesion is weaker than finite coherence [4], although these conditions are equivalent among planar Peano continua. Local finite cohesion is also implied by local cohesiveness [l2] in locally compact $ {T_2}$ spaces, and a converse holds if and only if the space is also rim connected. Our study answers a question of Whyburn about local cohesiveness.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0355998-5
Keywords: Local finite cohesion, finite coherence, local cohesiveness, rim connected, representation, k-canonical region, totally disconnected, quasicomponents, connectivity function, peripherally continuous, connectivity retract
Article copyright: © Copyright 1973 American Mathematical Society