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The Complexity of the Classification Problems of Finite-Dimensional Continua
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The Complexity of the Classification Problems of Finite-Dimensional Continua
classification
math.LO
math.GN
keywords
classificationcontinuacomplexityequivalencefinite-dimensionalproblemrelationscompare
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We consider the homeomorphic classification of finite-dimensional continua as well as several related equivalence relations. We show that, when $n \geq 2$, the classification problem of $n$-dimensional continua is strictly more complex than the isomorphism problem of countable graphs. We also obtain results that compare the relative complexity of various equivalence relations.
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