The Banach lattice C[0,1] is super d-rigid

Y. A. Abramovich; A. K. Kitover

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Displaying similar documents to “The Banach lattice C[0,1] is super d-rigid”

Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker (2007)

Fundamenta Mathematicae

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The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

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In this paper the context of independent sets $J_{L}^{p}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.

Every lattice is embeddable in the lattice of $T_{1}$ -topologies

Richard Valent (1973)

Colloquium Mathematicae

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On the lattice structure of $T_{1}$ topologies

T. G. Raghavan, I. L. Reilly (1986)

Matematički Vesnik

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Isomorphic and isometric copies of $ℓ_{\infty} (Γ)$ in duals of Banach spaces and Banach lattices

Marek Wójtowicz (2006)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ and $E$ be a Banach space and a real Banach lattice, respectively, and let $Γ$ denote an infinite set. We give concise proofs of the following results: (1) The dual space $X^{*}$ contains an isometric copy of $c_{0}$ iff $X^{*}$ contains an isometric copy of $ℓ_{\infty}$ , and (2) $E^{*}$ contains a lattice-isometric copy of $c_{0} (Γ)$ iff $E^{*}$ contains a lattice-isometric copy of $ℓ_{\infty} (Γ)$ .

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

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Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J_{L}^{p}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J_{L}^{p}$ .

The almost lattice isometric copies of $c_{0}$ in Banach lattices

Jinxi Chen (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper it is shown that if a Banach lattice $E$ contains a copy of $c_{0}$ , then it contains an almost lattice isometric copy of $c_{0}$ . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of $c_{0}$ in Banach spaces.

A visual approach to test lattices

Gábor Czédli (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let $p$ be a $k$ -ary lattice term. A $k$ -pointed lattice $L = (L; \lor, \land$ , $d_{1}, ..., d_{k})$ will be called a $p$ -lattice (or a test lattice if $p$ is not specified), if $(L; \lor, \land)$ is generated by ${d_{1}, ..., d_{k}}$ and, in addition, for any $k$ -ary lattice term $q$ satisfying $p (d_{1}, ..., d_{k})$ $\leq$ $q (d_{1}$ , $..., d_{k})$ in $L$ , the lattice identity $p \leq q$ holds in all lattices. In an elementary visual way, we construct a finite $p$ -lattice $L (p)$ for each $p$ . If $p$ is a canonical lattice term, then $L (p)$ coincides with the optimal $p$ -lattice of Freese, Ježek and Nation [Freese,...