Abstract
In many constructions with the method of Fedorčuk’s resolution, beginning with the first one in by Fedorčuk (English Trans Soviet Math Dokl 9:1148–1150, 1968), the value of the covering dimension is precisely determined, while for the corresponding value of inductive dimensions one has to be content with a mere estimate. In this chapter, we present a method of resolution which allows accurate computation of inductive dimensions. For certain classes of continua \(\mathcal {K}\) and certain pairs of integers m, n with m ≤ n, this method produces continua \(X_{m,n} \in \mathcal {K}\) with \(\dim X_{m,n} = m\) and ind X m,n = ind X m,n = n.
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Notes
- 1.
A continuum X is an Anderson–Choquet continuum if every non-degenerate subcontinuum of X admits only one embedding into X.
- 2.
A continuum X is a Cook continuum if every non-degenerate subcontinuum of X admits only one non-constant map into X.
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Charalambous, M.G. (2019). More Continua with Distinct Covering and Inductive Dimensions. In: Dimension Theory. Atlantis Studies in Mathematics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-22232-1_31
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DOI: https://doi.org/10.1007/978-3-030-22232-1_31
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