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Why the set $\{f \in \omega^\omega : \exists_{m}\forall_{m \leq n}^{}(f(n)\neq g(n))\}$ is $F_{\sigma}$ and meager?

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#general-topology #descriptive-set-theory #the-baire-space
629
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Prove that the Set $P$ of algebraic polynomial is a first category set in $C[a,b]$

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#real-analysis #analysis #baire-category #the-baire-space
62
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If a ball is the union of two sets, does one of them non empty interior?

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#general-topology #the-baire-space
112
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Confusion About Pointclasses

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#set-theory #descriptive-set-theory #the-baire-space
124
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Any $G \subseteq \mathbb{N}^\mathbb{N}$ is clopen

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#real-analysis #general-topology #metric-spaces #descriptive-set-theory #the-baire-space
211
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Are the basic open sets of the Baire space closed?

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#general-topology #descriptive-set-theory #the-baire-space
3.3k
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Baire space homeomorphic to irrationals

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#general-topology #measure-theory #continued-fractions #the-baire-space
720
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What can we say about closed sets in the Baire space that are neither open nor compact?

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#general-topology #descriptive-set-theory #the-baire-space
669
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Prove that Baire space $\omega^\omega$ is completely metrizable?

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#general-topology #metric-spaces #the-baire-space
2.8k
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What is the cardinality of $\omega^\omega$?

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#elementary-set-theory #cardinals #descriptive-set-theory #the-baire-space
290
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$\mathcal{N}^\omega$ is homeomorphic to $\mathcal{N}$, where $\mathcal{N}$ is Baire space.

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#general-topology #descriptive-set-theory #the-baire-space
101
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are the regular topology on $\mathbb R$ and the product topology on $\omega^\omega$ equivalent?

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#general-topology #descriptive-set-theory #the-baire-space
132
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Is the space $\mathbb N^ \mathbb N$ metrisable?

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#general-topology #metric-spaces #descriptive-set-theory #the-baire-space
106
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Is zero-dimensional, separable metric space a $\sigma$-space?

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#general-topology #metric-spaces #the-baire-space
1.1k
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Gale-Stewart Theorem (open games are determined) implies closed games are determined

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#set-theory #descriptive-set-theory #the-baire-space #infinite-games

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