Topographic spaces over ordered monoids
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A topography on a set is considered to be a collection of features described by two valuations: distance and elevation. Spaces with such structure will be studied on a general level, with generalized metric (gem) and pseudometric (pseudogem). We show many pseudogem distances and characteristics, particularly those related to the elevation function. We focus on paths in the topographic images and cohesiveness (generalized continuity) of their compositions with the elevation function. Special emphasis is also placed on the spaces arising from the digital geometry and, therefore, oering applications in image processing.
Document typePeer reviewed
Document versionFinal PDF
SourceMathematics for Applications. 2015 vol. 4, č. 1, s. 31-59. ISSN 1805-3629
- 2015/1