# On ${\stackrel{\u02c7}{H}}^{n}$-bubbles in n-dimensional compacta

Colloquium Mathematicae (1998)

- Volume: 75, Issue: 1, page 39-51
- ISSN: 0010-1354

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topKarimov, Umed, and Repovš, Dušan. "On $\check{H}^n$-bubbles in n-dimensional compacta." Colloquium Mathematicae 75.1 (1998): 39-51. <http://eudml.org/doc/210528>.

@article{Karimov1998,

abstract = {A topological space X is called an $\check\{H\}^n$-bubble (n is a natural number, $\check\{H\}^n$ is Čech cohomology with integer coefficients) if its n-dimensional cohomology $\check\{H\}^n(X)$ is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable $\check\{H\}^n$-bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any $\check\{H\}^2$-bubbles; and (3) Every n-acyclic finite-dimensional $L\check\{H\}^n$-trivial metrizable compactum contains an $\check\{H\}^n$-bubble.},

author = {Karimov, Umed, Repovš, Dušan},

journal = {Colloquium Mathematicae},

keywords = {locally connected spaces; low-dimensional compacta; Čech cohomology; bubble; slender group; locally connected space; slender groups},

language = {eng},

number = {1},

pages = {39-51},

title = {On $\check\{H\}^n$-bubbles in n-dimensional compacta},

url = {http://eudml.org/doc/210528},

volume = {75},

year = {1998},

}

TY - JOUR

AU - Karimov, Umed

AU - Repovš, Dušan

TI - On $\check{H}^n$-bubbles in n-dimensional compacta

JO - Colloquium Mathematicae

PY - 1998

VL - 75

IS - 1

SP - 39

EP - 51

AB - A topological space X is called an $\check{H}^n$-bubble (n is a natural number, $\check{H}^n$ is Čech cohomology with integer coefficients) if its n-dimensional cohomology $\check{H}^n(X)$ is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable $\check{H}^n$-bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any $\check{H}^2$-bubbles; and (3) Every n-acyclic finite-dimensional $L\check{H}^n$-trivial metrizable compactum contains an $\check{H}^n$-bubble.

LA - eng

KW - locally connected spaces; low-dimensional compacta; Čech cohomology; bubble; slender group; locally connected space; slender groups

UR - http://eudml.org/doc/210528

ER -

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