# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

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

### Tom 171 / 2002

Fundamenta Mathematicae 171 (2002), 101-116 MSC: Primary 54F15; Secondary 54G99, 54F50. DOI: 10.4064/fm171-2-1

#### Streszczenie

A compact metric space $\widetilde{X}$ is said to be a continuous pseudo-hairy space over a compact space $X\subset \widetilde{X}$ provided there exists an open, monotone retraction $r: \widetilde{X} \buildrel {\rm onto}\over\longrightarrow X$ such that all fibers $r^{-1}(x)$ are pseudo-arcs and any continuum in $\widetilde{X}$ joining two different fibers of $r$ intersects $X$. A continuum $Y_{X}$ is called a {\it continuous pseudo-fan of} a compactum $X$ if there are a point $c\in Y_{X}$ and a family ${\cal F}$ of pseudo-arcs such that $\bigcup {\cal F} = Y_{X}$, any subcontinuum of $Y_{X}$ intersecting two different elements of ${\cal F}$ contains $c$, and ${\cal F}$ 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 $X$.

#### Autorzy

• Janusz R. PrajsInstitute of Mathematics
Opole University
Oleska 48
45-052 Opole, Poland