query: Extending linear functionals by induction
positive_passages.docid: 26183
positive_passages.text: Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
negative_passages.docid: 71140
negative_passages.text: Pointwise limit of the sequence of continuously differentiable functions defined inductively.
negative_passages.docid: 44148
negative_passages.text: Functions that are their own inverse.
negative_passages.docid: 137907
negative_passages.text: Composing functors with natural transformations
negative_passages.docid: 93342
negative_passages.text: Show that $\neg$ and $\wedge$ form a functionally complete collection of logical operators.
negative_passages.docid: 84448
negative_passages.text: Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $
negative_passages.docid: 77507
negative_passages.text: Induction without a base case
negative_passages.docid: 103924
negative_passages.text: Kernel of a substitution map
negative_passages.docid: 50037
negative_passages.text: Proving that kernels of evaluation maps are generated by the $x_i - a_i$
negative_passages.docid: 137012
negative_passages.text: Mathematical Induction for Recurrence Relation
negative_passages.docid: 61939
negative_passages.text: Induction of inequality involving AP
negative_passages.docid: 120170
negative_passages.text: A late-diverging "approximating solution" for a system of functional equations
negative_passages.docid: 123519
negative_passages.text: Fréchet differentiability from Gâteaux differentiability
negative_passages.docid: 31900
negative_passages.text: Induction on Real Numbers
negative_passages.docid: 104914
negative_passages.text: Abount linear functional: If $T(B)$ is bounded, is $T$ bounded?
negative_passages.docid: 136909
negative_passages.text: Functional Analysis: The rank of an operator detemines if it's a compact operator.
negative_passages.docid: 78344
negative_passages.text: Nonconstant linear functional on a topological vector space is an open mapping