Topology
In topology, a metric space can be constructed by defining a similarity instead of a distance. The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity: the closer the points, the lesser the distance).
The definition of the similarity can vary among authors, depending on which properties are desired. The basic common properties are
- Positive defined:
- Majored by the similarity of one element on itself (auto-similarity): and
More properties can be invoked, such as reflectivity or finiteness . The upper value is often set at 1 (creating a possibility for a probabilistic interpretation of the similitude).
Read more about this topic: Similarity (geometry)