# On the disjoint (0,N)-cells property for homogeneous ANR's

Colloquium Mathematicae (1993)

- Volume: 66, Issue: 1, page 77-84
- ISSN: 0010-1354

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topKrupski, Paweł. "On the disjoint (0,N)-cells property for homogeneous ANR's." Colloquium Mathematicae 66.1 (1993): 77-84. <http://eudml.org/doc/210236>.

@article{Krupski1993,

abstract = {A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell $B^\{n\}$ into X and for each ε > 0 there exist a point y ∈ X and a map $g:B^\{n\} → X$ such that ϱ(x,y) < ε, $\widehat\{ϱ\}(f,g) < ε$ and $y ∉ g(B^\{n\})$. It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact $LC^\{n-1\}$-space then local homologies satisfy $H_\{k\}(X,X-x) = 0$ for k < n and Hn(X,X-x) ≠ 0.},

author = {Krupski, Paweł},

journal = {Colloquium Mathematicae},

keywords = {generalized manifold; homogeneous space; disjoint cells property; absolute neighborhood retract; $LC^n$-space; -space},

language = {eng},

number = {1},

pages = {77-84},

title = {On the disjoint (0,N)-cells property for homogeneous ANR's},

url = {http://eudml.org/doc/210236},

volume = {66},

year = {1993},

}

TY - JOUR

AU - Krupski, Paweł

TI - On the disjoint (0,N)-cells property for homogeneous ANR's

JO - Colloquium Mathematicae

PY - 1993

VL - 66

IS - 1

SP - 77

EP - 84

AB - A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell $B^{n}$ into X and for each ε > 0 there exist a point y ∈ X and a map $g:B^{n} → X$ such that ϱ(x,y) < ε, $\widehat{ϱ}(f,g) < ε$ and $y ∉ g(B^{n})$. It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact $LC^{n-1}$-space then local homologies satisfy $H_{k}(X,X-x) = 0$ for k < n and Hn(X,X-x) ≠ 0.

LA - eng

KW - generalized manifold; homogeneous space; disjoint cells property; absolute neighborhood retract; $LC^n$-space; -space

UR - http://eudml.org/doc/210236

ER -

## References

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