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Interval Topology and Order‐Convergence in the Hyperspace of a Topological Space
Author(s) -
Schmidt HansJürgen
Publication year - 1984
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.19841180108
Subject(s) - hyperspace , mathematics , topology (electrical circuits) , topological space , interval (graph theory) , space (punctuation) , convergence (economics) , general topology , product topology , order (exchange) , weak topology (polar topology) , connected space , closed set , pure mathematics , discrete mathematics , combinatorics , extension topology , computer science , finance , economics , economic growth , operating system
In the hyperspace Exp X of all closed subsets of a topological space X interval and order topology solely use the ⊂‐relation in Exp X for their definitions whereas H AUSDORFF set convergence and V IETORIS topology use neighbourhoods in X itself. Nevertheless there exist intimate but non‐trivial relations between them.
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