Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs. "Continuous pseudo-hairy spaces and continuous pseudo-fans." Fundamenta Mathematicae 171.2 (2002): 101-116. <http://eudml.org/doc/286134>.

@article{JanuszR2002,
abstract = {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.},
author = {Janusz R. Prajs},
journal = {Fundamenta Mathematicae},
keywords = {compact metric space; continuous decomposition of compactum; pseudo-arc; pseudo-hairy space; pseudo-fan},
language = {eng},
number = {2},
pages = {101-116},
title = {Continuous pseudo-hairy spaces and continuous pseudo-fans},
url = {http://eudml.org/doc/286134},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Janusz R. Prajs
TI - Continuous pseudo-hairy spaces and continuous pseudo-fans
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 2
SP - 101
EP - 116
AB - 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.
LA - eng
KW - compact metric space; continuous decomposition of compactum; pseudo-arc; pseudo-hairy space; pseudo-fan
UR - http://eudml.org/doc/286134
ER -