Metadata
Mathematics Graduate Understand Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Understand

  • Difficulty estimate

    Medium

  • Tags

    functional analysis, Banach spaces, weak convergence, weak*, Banach-Alaoglu, reflexivity

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' understanding of weak and weak* convergence in Banach spaces: formal definitions (nets and sequences), relationships between weak and weak* topologies, characterizations via continuous linear functionals, key results (Banach-Alaoglu, Eberlein-Smulian, reflexivity criteria), typical examples and counterexamples (l^p, c0, L^p, dual spaces), uniqueness and lower semicontinuity properties of limits, and short proofs or constructions illustrating convergence and compactness.
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.