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A Hilbert cube compactification of the function space with the compact-open topology

Atsushi Kogasaka, Katsuro Sakai (2009)

Open Mathematics

Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification C ¯ (X) of C(X) such that the pair ( C ¯ (X), C(X)) is homeomorphic to (Q, s). In case...

A Kleinecke-Shirokov type condition with Jordan automorphisms

Matej Brešar, Ajda Fošner, Maja Fošner (2001)

Studia Mathematica

Let φ be a Jordan automorphism of an algebra . The situation when an element a ∈ satisfies 1 / 2 ( φ ( a ) + φ - 1 ( a ) ) = a is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson’s lemma.

A Kratzel's integral transformation of distributions.

J. A. Barrios, J. J. Betancor (1991)

Collectanea Mathematica

In this paper we study an integral transformation introduced by E. Kratzel in spaces of distributions. This transformation is a generalization of the Laplace transform. We employ the usually called kernel method. Analyticity, boundedness, and inversion theoremes are established for the generalized transformation.

A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ ¹ ( ℤ ₊ k )

F. Gourdeau, Z. A. Lykova, M. C. White (2005)

Studia Mathematica

We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly...

A Lifting Result for Locally Pseudo-Convex Subspaces of L₀

Félix Cabello Sánchez (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that if F is a topological vector space containing a complete, locally pseudo-convex subspace E such that F/E = L₀ then E is complemented in F and so F = E⊕ L₀. This generalizes results by Kalton and Peck and Faber.

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