Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\) (Q386227)
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scientific article; zbMATH DE number 6236605
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\) |
scientific article; zbMATH DE number 6236605 |
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Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\) (English)
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9 December 2013
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Many theorems in (General) Topology and Analysis rely on some (weak) form of the axiom of choice. The authors show that some results on connectedness and dimension need some choice as well. Examples include: non-trivial connected separable metric spaces have size continuum; every locally connected metric continuum is separable; every connected subspace of the plane is separable, and many more.
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axiom of choice
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connected separable metric space
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punctiform
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totally imperfect
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Menger-Moore-Mazurkiewicz theorem
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