Displaying similar documents to “The Lie algebra of a nuclear group.”

Concrete subspaces and quotient spaces of locally convex spaces and completing sequences

Süleyman Önal, Tosun Terzioğlu

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CONTENTSIntroduction..................................................................................51. Almost bounded sets and operators........................................62. Eidelheit’s theorem................................................................133. Nuclear Köthe quotients.........................................................204. Nuclear Köthe subspaces and completing sequences...........225. Applications...........................................................................256....

Fréchet directional differentiability and Fréchet differentiability

John R. Giles, Scott Sciffer (1996)

Commentationes Mathematicae Universitatis Carolinae

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Zaj’ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable...

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...