## Local finite cohesion

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- by W. C. Chewning PDF
- Trans. Amer. Math. Soc.
**176**(1973), 385-400 Request permission

## 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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## Additional Information

- © Copyright 1973 American Mathematical Society
- 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