Search results for "Pseudo-arc"
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A continuous decomposition of the Menger curve into pseudo-arcs
2000
It is proved that the Menger universal curve M admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to M. Wilson proved [8] Anderson's announcement [1] saying that for any Peano continuum X the Menger universal curve M admits a continuous decomposition into homeomorphic copies of M such that the quotient space is homeomorphic to X. Anderson also announced (unpublished) that the plane admits a continuous decomposition into pseudo-arcs. This result was proved by Lewis and Walsh [4]. In a previous paper [6] the author has proved that each locally planar Peano continuum with no local separating point admits a continuous decomposition into pseudo-arcs. Applying…
A continuous circle of pseudo-arcs filling up the annulus
1999
We prove an early announcement by Knaster on a decomposition of the plane. Then we establish an announcement by Anderson saying that the plane annulus admits a continlous decomposition into pseudo-arcs such that the quotient space is a simple closed curve. This provides a new plane curve, "a selectible circle of pseudo-aics", and answers some questions of Lewis.