
TL;DR
The paper establishes conditions under which a complete metric space is an ANR or AR based on intersection properties of open balls with bounded or unbounded centers, and provides a criterion for incomplete spaces.
Contribution
It introduces new intersection-based criteria for identifying ANRs and ARs in metric spaces, including incomplete spaces.
Findings
Complete metric spaces with bounded intersection properties are ANRs.
Unbounded intersection conditions imply the space is an AR.
A criterion for incomplete spaces to be ANRs or ARs is provided.
Abstract
It is shown that if for a complete metric space there is a constant such that the intersection of open balls is nonempty for every finite system of centers and a corresponding system of radii such that and (), then is an ANR; and if in the above one may put , the space is an AR. A certain criterion for an incomplete metric space to be an A(N)R is presented.
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