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Continuous decompositions of Peano plane continua into pseudo-arcs

Janusz Prajs (1998)

Fundamenta Mathematicae

Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction r : X ̃ o n t o X such that all fibers r - 1 ( x ) are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum Y X is called a continuous pseudo-fan of a compactum X if there are a point c Y X and a family ℱ of pseudo-arcs such that = Y X , any subcontinuum of Y X intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...

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