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## Fundamenta Mathematicae

2002 | 171 | 2 | 101-116

## Continuous pseudo-hairy spaces and continuous pseudo-fans

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.

101-116

wydano
2002

### Twórcy

autor
• 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.