On a method of constructing ANR-sets. An application of inverse limits

Krasinkiewicz, J.

doi:10.4064/fm-92-2-95-112

Cited by 17 publications

(14 citation statements)

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“…[10]). Let P * be the quotient space of P by lim ← − P. Obviously, the space P * is homeomorphic to the one-point…”

Section: The Construction Of Examples and The Proofs Of The Main Resultsmentioning

confidence: 99%

On noncontractible compacta with trivial homology and homotopy groups

Karimov¹,

Repovš²

2009

Proc. Amer. Math. Soc.

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Abstract. We construct an example of a Peano continuum X such that: (i) X is a one-point compactification of a polyhedron; (ii) X is weakly homotopy equivalent to a point (i.e. π n (X) is trivial for all n ≥ 0); (iii) X is noncontractible; and (iv) X is homologically and cohomologically locally connected (i.e. X is an HLC and clc space). We also prove that all classical homology groups (singular,Čech, and Borel-Moore), all classical cohomology groups (singular andČech), and all finite-dimensional Hawaiian groups of X are trivial.

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“…[10]). Let P * be the quotient space of P by lim ← − P. Obviously, the space P * is homeomorphic to the one-point…”

Section: The Construction Of Examples and The Proofs Of The Main Resultsmentioning

confidence: 99%

On noncontractible compacta with trivial homology and homotopy groups

Karimov¹,

Repovš²

2009

Proc. Amer. Math. Soc.

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“…[7,11]) and let P be its natural compactification by the Case-Chamberlin continuum C. Let P * be the quotient space of P by C.…”

Section: Preliminariesmentioning

confidence: 99%

On the fundamental group of R^3 modulo the Chase-Chaberlin continuum

Eda¹,

Karimov²,

Repovš

2007

Glas. Mat. Ser. III

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“…Firstly, we define some kinds of dendrites by the following general method (see [2]): Let X be a 0-dimensional compact metric space and let g : X -> X be any map of X. Choose an inverse sequence X = {X,,, p nM+ \ \n = 1, 2 , .…”

Section: Theorem 31 For Any Countable Ordinal Number X There Is a mentioning

confidence: 99%

“…(2) For any countable ordinal number k there is a map / of a disk B 2 such that [2] The depth of centres of maps on dendrites 45 (3) For any countable ordinal number k there is a homeomorphism h :…”

Section: Introductionmentioning

confidence: 99%

The depth of centres of maps on dendrites

Kato¹

1998

J Aust Math Soc A

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Xiong proved that if / : / -> / is any map of the unit interval /, then the depth of the centre of / is at most 2, and Ye proved that for any map / : T ->• T of a finite tree T, the depth of the centre of / is at most 3. It is natural to ask whether the result can be generalized to maps of dendrites. In this note, we show that there is a dendrite D such that for any countable ordinal number X there is a map / : D -> D such that the depth of centre of / is k. As a corollary, we show that for any countable ordinal number X there is a map (respectively a homeomorphism) / of a 2-dimensional ball B 2 (respectively a 3-dimensional ball 5 3 ) such that the depth of centre of / is A.1991 Mathematics subject classification (Amer. Math. Soc): primary 54H20; secondary 58F50.

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On a method of constructing ANR-sets. An application of inverse limits

Cited by 17 publications

References 0 publications

On noncontractible compacta with trivial homology and homotopy groups

On noncontractible compacta with trivial homology and homotopy groups

On the fundamental group of R^3 modulo the Chase-Chaberlin continuum

The depth of centres of maps on dendrites

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