Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

## Kernel Projections and Quotient Lattices

Piotr Rudnicki
University of Alberta, Edmonton
This work was partially supported by NSERC Grant OGP9207 and NATO CRG 951368.

### Summary.

This article completes the Mizar formalization of Chapter I, Section 2 from [13]. After presenting some preliminary material (not all of which is later used in this article) we give the proof of theorem 2.7 (i), p.60. We do not follow the hint from [13] suggesting using the equations 2.3, p. 58. The proof is taken directly from the definition of continuous lattice. The goal of the last section is to prove the correspondence between the set of all congruences of a continuous lattice and the set of all kernel operators of the lattice which preserve directed sups (Corollary 2.13).

#### MML Identifier: WAYBEL20

The terminology and notation used in this paper have been introduced in the following articles [21] [10] [24] [25] [26] [17] [27] [7] [9] [8] [12] [20] [19] [22] [6] [1] [23] [2] [18] [3] [14] [28] [15] [4] [11] [5] [16]

#### Contents (PDF format)

1. Preliminaries
2. Some Remarks on Lattice Product
3. Kernel Projections and Quotient Lattices

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