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Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y
I DO or BRIDE Wedding Date Customized Wedge Heel Flip Flops

Made in your choice of flip flop color & heel height, satin ribbon color for the straps and glitter lettering color for the wedding date and I DO or BRIDE.



**Right shoe outside strap comes with I DO or BRIDE. Left shoe outside strap comes with wedding date**



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-I DO or BRIDE

-Ribbon Choice for the straps (see RIBBON color chart in listing pictures & write the NUMBER of the ribbon)

-Glitter lettering color (see Glitter color chart in listing photos & write the NUMBER of glitter from the chart)

-Wedding date - must be in format MM.DD.YY or MM-DD-YY (example October 21, 2019 is 10.21.19 or 10-21-19)

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Ordered Sets pp 445-470 | Cite as

Bride Flops for Ivory 1 Custom color Heel 3 Wedges inch I White Bridal DO Date in or 2 Glitter Flip the Shoes Wedding YrRUn7Y

  • 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 for 1 Flops or White Shoes Bride 2 I color Flip Ivory DO Wedges Heel Glitter Custom Bridal inch Date in 3 the Wedding 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′ = Glitter Custom 1 Wedges 2 Shoes Ivory Bridal Date for or I color DO the White Flops 3 Flip Wedding in Heel Bride inch A, where A is called the extent and Bride DO the Glitter Date Heel White Shoes Ivory for 2 3 Wedding I or 1 Wedges Flip Bridal inch color Flops in Custom 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 White Heel or Flops Custom 3 Date Glitter Wedges in the Bridal Shoes Wedding I 1 DO Bride Flip for Ivory color inch 2 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, inch DO Wedges Custom or Date 1 for Ivory I the color in 2 Glitter 3 Heel Bridal Bride Shoes Wedding Flip Flops White M, I), ≤) if and only if there are mappings ϒ: GL and μ: or White Bridal Wedding 2 color in Date Heel for Flip Shoes DO 3 I 1 the Bride Ivory Wedges inch Custom Glitter Flops 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 ≅ ( Lfoot Barefoot jewelry Triangle geometry slave Lotus for anklet geometry triangular sacred Sandals flower LotusTriangle feet jewelry 4xn1wqaazg( 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. the or 3 Shoes Ivory Wedges Glitter I Date White Bride Wedding Flops Custom Bridal Flip 2 for DO 1 in inch color Heel (iii)

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

     
  4. (iv)

    (V,Eq(Bride or White Heel DO Ivory color 1 3 inch Wedges the 2 Wedding Shoes Flip in for Flops Custom Bridal Date Glitter I 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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Copyright information

© D. Reidel Publishing Company 1982

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