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Why is the real line not used in Descriptive Set Theory?

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#general-topology #set-theory #descriptive-set-theory
453
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Universal sets in metric spaces

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#set-theory #descriptive-set-theory
3.5k
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Countable compact spaces as ordinals

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#general-topology #compactness #ordinals #descriptive-set-theory
692
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How do you find the smallest of homeomorphic ordinals?

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#general-topology #ordinals #descriptive-set-theory
472
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Borel sets and clopen decompositions

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#general-topology #measure-theory #descriptive-set-theory
1.6k
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Derived sets and ordinals

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#real-analysis #ordinals #descriptive-set-theory
670
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Doubt in Kechris's Classical Descriptive Set Theory

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#general-topology #descriptive-set-theory #baire-category
215
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Sets invariant under sections

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#general-topology #set-theory #descriptive-set-theory
4.1k
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Compact subset of an open set

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#general-topology #functional-analysis #metric-spaces #descriptive-set-theory
686
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$\Sigma_{\alpha+1}^0(X)$ universal set based on the Baire space

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#set-theory #descriptive-set-theory #the-baire-space
339
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Separable metric space with 0-dimensional kernel

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#general-topology #set-theory #descriptive-set-theory
1.8k
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Two questions about the Cantor set construction

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#real-analysis #general-topology #descriptive-set-theory
782
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Does every infinite $\Sigma^1_1$ set have an infinite $\Delta^1_1$ subset?

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#logic #computability #descriptive-set-theory
17.9k
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The $\sigma$-algebra of subsets of $X$ generated by a set $\mathcal{A}$ is the smallest sigma algebra including $\mathcal{A}$

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#descriptive-set-theory #measure-theory
3.9k
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Cantor space: example of an open set that's not closed?

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#general-topology #examples-counterexamples #descriptive-set-theory

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