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Lattices which can be represented as lattices of intervals

Vaggelis Felouzis

Abstract

We investigate lattices that can be represented as sublattices of the lattice of all convex subsets of a linearly ordered set $(X, \leq)$ and as lattices of convex subsets of $(X, \leq)$. A representation theory for general lattices is presented and also some applications in general topology are given.

Lattices which can be represented as lattices of intervals

Abstract

We investigate lattices that can be represented as sublattices of the lattice of all convex subsets of a linearly ordered set and as lattices of convex subsets of . A representation theory for general lattices is presented and also some applications in general topology are given.

Paper Structure

This paper contains 4 sections, 22 theorems, 25 equations.

Table of Contents

  1. Introduction and the main result
  2. Loc-lattices of sets
  3. Semi prime filters and Proof of Theorem \ref{['ath']}
  4. some applications in general topology.

Key Result

Theorem 1.3

Theorems & Definitions (72)

  • Definition 1.1
  • Definition 1.2
  • Theorem 1.3
  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Remark 2.4
  • Theorem 2.5
  • Lemma 2.6
  • proof
  • ...and 62 more