AANR spaces and absolute retracts for tree-like continua

Title:

AANR spaces and absolute retracts for tree-like continua

Creator:

Charatonik, Janusz Jerzy and Prajs, Janusz R.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7c6fc16a-9674-42b3-9801-822c6500d00d
uuid:7c6fc16a-9674-42b3-9801-822c6500d00d

Subject:

AANR, absolute retract, arc component, arc-like;, continuum, decomposable, dendroid, hereditarily unicoherent, retraction, terminal continuum, and tree-like

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, $\lambda $-dendroids, dendroids, arc-like continua and arc-like $\lambda $-dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

877-891

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:4

Harvested from:

CDK

Metadata only:

false