We provide some properties and characterizations of homologically UV n -maps and lc G n -spaces. We show that there is a parallel between recently introduced by Cauty  algebraic ANR's and homologically lc G n -metric spaces, and this parallel is similar to the parallel between ordinary ANR's and LC n -metric spaces. We also show that there is a similarity between the properties of LC n -spaces and lc G n -spaces. Some open questions are raised.
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