Abstract
Here we digress somewhat, although fixed point theory in geodesic spaces is an important underlying factor. A finitely compact (recall, this means bounded closed sets are compact) geodesically connected (metrically convex) metric space \(\left (R,d\right )\) which has the geodesic extension property (see Definition 9.3 below) and for which such extension is unique is called a G-space .
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Notes
- 1.
The reviewer of this paper states in [188]: “Without any doubt this is one of the nicest papers in geometric topology of the 1990’s.”
- 2.
A metric space is said to have Alexandrov curvature ≤κ if it is locally a CAT\(\left (\kappa \right )\) space. CAT \(\left (\kappa \right )\) spaces are defined in the next chapter.
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Kirk, W., Shahzad, N. (2014). The G-Spaces of Busemann. In: Fixed Point Theory in Distance Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-10927-5_8
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