Abstract
A set M is locally connected at a point p ∊ M provided that if U p is any open set about p 9 then there exists an open set V p , p ∊ V p ⊂ U p9 such that each point of M ∩ V p lies together with p in a connected subset of M ∩ U p .
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsBibliography
H. Hahn, Über die Kompomenten offenen Mengen, Fundamenta Mathematicae, vol. 2 (1921), pp. 189–192.
K. Kuratowski, Une définition topologique de la ligne de Jordan, Fundamenta Mathe-maticae, vol. 1 (1920), pp. 40–43.
R. L. Moore, Report on continuous curves from the viewpoint of analysis situs, Bulletin of the American Mathematical Society, vol. 29 (1923), pp. 289–302.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Whyburn, G., Duda, E. (1979). Locally Connected Sets. In: Dynamic Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6262-3_14
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6262-3_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-6264-7
Online ISBN: 978-1-4684-6262-3
eBook Packages: Springer Book Archive