Geodesic
A continuous operator extending fuzzy ultrametrics
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 611-622.

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We consider the problem of simultaneous extension of fuzzy ultrametrics defined on closed subsets of a complete fuzzy ultrametric space. We construct an extension operator that preserves the operation of pointwise minimum of fuzzy ultrametrics with common domain and an operation which is an analogue of multiplication by a constant defined for fuzzy ultrametrics. We prove that the restriction of the extension operator onto the set of continuous, partial fuzzy ultrametrics is continuous with respect to the Hausdorff metric topology.
Classification : 54A40, 54C20, 54E70
Keywords: fuzzy ultrametric; continuous extension operator; Hausdorff metric 
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Stasyuk, I.; Tymchatyn, E. D. A continuous operator extending fuzzy ultrametrics. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 611-622. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a10/