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Q(set of rationals) is of baire's first category in itself but N(natural numbers) are of second category in itself .

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#real-analysis #baire-category #the-baire-space
210
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$\Bbb R^J$ is a Baire space in product topology

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#general-topology #proof-verification #proof-explanation #product-space #the-baire-space
67
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A question regarding the convergence of a sequence of functions at some point on $[0,1]$

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#general-topology #analysis #the-baire-space
29
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A subset of the second Baire category on the real line

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#baire-category #the-baire-space
123
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Continuous parametrization of continuous functions in the Baire space $\omega^\omega$

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#set-theory #solution-verification #descriptive-set-theory #the-baire-space
51
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Operation over the Baire space $\omega^\omega$ that preserves Borel sets

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#set-theory #descriptive-set-theory #borel-sets #the-baire-space
144
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Showing $A\cap B \ne \emptyset$

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#general-topology #elementary-set-theory #metric-spaces #the-baire-space
110
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Wadge Hierarchy on $\Delta^{0}_{2}$ sets

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#descriptive-set-theory #the-baire-space
74
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Clarification of Baire category theorem: a (counter-?)example

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#functional-analysis #metric-spaces #the-baire-space
226
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Is every Polish space the quotient of some subset of Baire space?

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#descriptive-set-theory #the-baire-space
150
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Something about the Baire Space

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#real-analysis #metric-spaces #the-baire-space
65
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$T$ linear. $T$ is bounded if, and only if, $int(T^{-1}(\overline{B_{N_2}}(0,1))) \neq \emptyset$R

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#functional-analysis #analysis #the-baire-space
103
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Is there a perfect Polish topology on the Baire space that is strictly finer than the usual topology?

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#metric-spaces #descriptive-set-theory #the-baire-space
103
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Reference request: lattice theory of the algebra of open sets in a subspace of the Baire space

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#general-topology #reference-request #lattice-orders #descriptive-set-theory #the-baire-space
234
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Application of Baire theorem in complete metric space

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#general-topology #the-baire-space

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