### A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension

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A retractible non-locally connected dendroid is constructed.

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...

For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an ${L}_{ch}$-extender (resp. ${L}_{cch}$-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 ${L}_{ch}$-extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...