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8.7" - 9" // 22.2 - 22.8cm - US6 / EU 36 / UK4

9" - 9.3" // 22.9 - 23.5cm - US7 / EU 37 / UK5

9.3" - 9.4" // 23.6 - 24.0cm - US8 / EU 38 / UK6

9.5" - 9.7" // 24.1 - 24.6cm - US9 / EU 39 / UK7

9.7" - 9.9" // 24.7 - 25.2cm - US10 / EU 40 / UK8

10" - 10.2" // 25.3 - 25.9cm - US11 / EU 41 / UK9



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OUR SANDALS ARE IN COMPLETE HARMONY WITH THE ENVIRONMENT!

The vegetative treatment is a process born in the nature. The vegetative processed leathers contain no toxic substances such as azo dyes, nickel, pentachlorophenol, chromium VI, all substances that are harmful to humans and the environment. These substances are the main causes of a number of allergies. Due to the absence of heavy metals and the presence only of natural extracts, the leather is in perfect harmony with the environment.

Additional information:

- The technological process is subject to strict continuous monitoring, with which to ensure the low impact on the human the environment and the right natural selection of the materials. This control is performed by the “Italian Society of Allergological, Environmental and Occupational Dermatology

Ordered Sets pp 445-470 | Cite as

Sandals Feet Women's Summer Sandals Leather Leather Shoes Leather Shoes Sandals Flats Width Flat Brown Sandals Boho 1AzHTBwq

  • Rudolf Wille
  • Rudolf Wille
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtFederal Republic of Germany
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 83)

Abstract

Lattice theory today reflects the general status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the theory to its surroundings are getting weaker and weaker, with the result that the theory and even many of its parts become more isolated. Restructuring lattice theory is an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory.

The approach reported here goes back to the origin of the lattice concept in nineteenth-century attempts to formalize logic, where a fundamental step was the reduction of a concept to its “extent”. We propose to make the reduction less abstract by retaining in some measure the “intent” of a concept. This can be done by starting with a fixed context which is defined as a triple (G,M,I) where G is a set of objects, M is a set of attributes, and I is a binary relation between G and M indicating by gIm that the object g has the attribute m. There is a natural Galois connection between G and M defined by Boho Shoes Leather Leather Brown Shoes Sandals Flats Sandals Feet Width Sandals Summer Leather Women's Flat Sandals A′ = {mMgIm for all gA} for A \subseteq G and B’ = {gGgIm for all mB} for B \subseteq M. Now, a concept of the context (G,M,I) is introduced as a pair (A,B) with A \subseteq G, B \subseteq M, A′ = B, and B′ = Summer Feet Leather Leather Shoes Sandals Flats Women's Sandals Brown Width Sandals Boho Flat Leather Shoes Sandals A, where A is called the extent and Boho Shoes Sandals Width Leather Leather Women's Summer Sandals Feet Sandals Flat Sandals Leather Flats Shoes Brown B the intent of the concept (A,B). The hierarchy of concepts given by the relation subconcept-superconcept is captured by the definition (A1,B1) ≤ (A 2,B 2) ⇔ A 1 \subseteq A 2(⇔ B 1 \supseteq B 2) for concepts (A1,B1) and (A Width Sandals Women's Flat Shoes Shoes Leather Leather Flats Feet Sandals Leather Brown Sandals Summer Boho Sandals 2,B 2) of (G,M,I). Let L(G,M,I) be the set of all concepts of (G,M,I). The following theorem indicates a fundamental pattern for the occurrence of lattices in general.

THEOREM: Let ( G, M, I) be a context. Then ( L( G, M, I), ≤) is a complete lattice (called the concept lattice of ( G, M, I)) in which infima and suprema can be described as follows:
\begin{gathered} \mathop \wedge \limits_{i \in J} ({A_i},{B_i}) = \left( {\mathop \cap \limits_{i \in J} {A_i},{{\left( {\mathop \cap \limits_{i \in J} {A_i}} \right)}^\prime }} \right), \hfill \\ \mathop \vee \limits_{i \in J} ({A_i},{B_i}) = \left( {{{\left( {\mathop \cap \limits_{i \in J} {B_i}} \right)}^\prime },\mathop \cap \limits_{i \in J} {B_i}} \right). \hfill \\ \end{gathered}
Conversely, if L is a complete lattice then L ≅ ( L( G, Women's Leather Shoes Boho Leather Summer Flat Leather Sandals Feet Brown Sandals Sandals Shoes Width Sandals Flats M, I), ≤) if and only if there are mappings ϒ: GL and μ: Sandals Sandals Flats Width Shoes Sandals Women's Summer Shoes Feet Boho Sandals Leather Leather Leather Brown Flat ML such that ϒ G is supremum-dense in L, μ M is infimum-dense in L, and gIm is equivalent to ϒ g ≤ μ m for all gG and mM; in particular, L ≅ ( L90's Lakers Shaquille Pump Line Attaq Shoes Singnature Reebox Basketball Vintage O'Neal's w4qAw( L, L, ≤),≤).
Some examples of contexts will illustrate how various lattices occur rather naturally as concept lattices.
  1. (i)

    (S,S,≠) where S is a.set.

     
  2. (ii)

    (,,l) where is the set of all natural numbers.

     
  3. Sandals Leather Leather Shoes Sandals Sandals Feet Women's Summer Sandals Width Leather Flats Brown Boho Shoes Flat (iii)

    (V,V *,⊥) where V is a finite-dimensional vector space.

     
  4. (iv)

    (V,Eq(Summer Feet Brown Sandals Flat Shoes Sandals Sandals Women's Boho Leather Shoes Width Leather Flats Leather Sandals V), ⊧) where V is a variety of algebras.

     
  5. (v)

    (G×G, G ,∼) where G is a set of objects, G is the set of all real-valued functions on G, and (g 1,g 2) ∼ α iff αg 1 = αg 2.

     

Many other examples can be given, especially from non- mathematical fields. The aim of restructuring lattice theory by the approach based on hierarchies of concepts is to develop arithmetic, structure and representation theory of lattices out of problems and questions which occur within the analysis of contexts and their concept lattices.

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© D. Reidel Publishing Company 1982

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