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Characterization of Compact Sets by Their Dilation Volume
Author(s) -
Rataj Jan
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951730116
Subject(s) - mathematics , dilation (metric space) , uniqueness , homeomorphism (graph theory) , characterization (materials science) , locally compact space , compact space , pure mathematics , topological space , euclidean space , network topology , topology (electrical circuits) , discrete mathematics , mathematical analysis , combinatorics , computer science , materials science , nanotechnology , operating system
The uniqueness up to translation of the characterization of random compact sets in Euclidean space by their dilation volumes is shown. The unique correspondence is shown to be a homeomorphism with respect to suitable topologies. If set differences of volume zero are neglected, dilations by three‐point sets are sufficient to determine a non‐random compact set and the correspondence is again a homeomorphism with respect to vague topologies.