Continuous pseudo-hairy spaces and continuous pseudo-fans

• Autorzy: Janusz R. Prajs
• Języki publikacji: EN

Abstrakty

EN

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 $r: X̃ {onto \atop ⟶ } X$ 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 $⋃ ℱ = Y_{X}$, any subcontinuum of $Y_{X}$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with respect to the Hausdorff metric). It is proved that for each compact metric space X there exist a continuous pseudo-hairy space over X and a continuous pseudo-fan of X.

Kategorie tematyczne

• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54G99: None of the above, but in this section
• 54F15: Continua and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 2
• Strony: 101-116

Daty

wydano

2002

Twórcy

autor

Janusz R. Prajs

• Institute of Mathematics, Opole University, Oleska 48, 45-052 Opole, Poland, Current address, Department of Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A.

Identyfikatory

DOI

10.4064/fm171-2-1