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AANR spaces and absolute retracts for tree-like continua

Janusz Jerzy Charatonik, Janusz R. Prajs (2005)

Czechoslovak Mathematical Journal

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, λ -dendroids, dendroids, arc-like continua and arc-like λ -dendroids is an approximative absolute...

Dugundji extenders and retracts on generalized ordered spaces

Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)

Fundamenta Mathematicae

For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an L c h -extender (resp. L c c h -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous L c h -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...

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