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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Rendiconti del Circo...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Rendiconti del Circolo Matematico di Palermo (1952 -)
Article . 1999 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1999
Data sources: zbMATH Open
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Ultra smooth continua are smooth

Authors: Charatonik, Janusz J.;

Ultra smooth continua are smooth

Abstract

A continuum \(X\) is said to be smooth at a point \(p \in X\) if it is hereditarily unicoherent at \(p\) and for each \(x \in X\) and each sequence \(\{x_n\}\) converging to \(x\) the sequence of irreducible continua \(\{I(p,x_n)\}\) converges to the irreducible continuum \(I(p,x).\) \(X\) is said to be smooth if it is smooth at some point. A continuum \(X\) is said to be ultra smooth at a point \(p \in X\) if it is hereditarily unicoherent at \(P\) and for every pair of points \(x\) and \(y\) of \(X\) there exists a retraction of \(X\) onto the subcontinuum \(Y = I(p,x) \cup I(P,y)\) preserving the weak cutpoint order. The author shows that if a continuum \(X\) is ultra smooth at a point \(p\) then it is smooth at \(p.\) It is known by an example of \textit{Lewis Lum} [Stud. Topol., Proc. Conf. Charlotte, N.C., 1974, 331-338 (1975; Zbl 0306.54050)] that the converse is false even for dendroids. The author also characterizes ultra smooth continua which are formed as the union of a null sequence of irreducible continua.

Related Organizations
Keywords

hereditarily unicoherent, Continua and generalizations, Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, weak cutpoint order, continuum, Unicoherence, multicoherence, irreducible

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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