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Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin Gutev, Vesko Valov (1994)

Fundamenta Mathematicae

The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is L C n - 1 C n - 1 (resp., L C n - 1 ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

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.

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