Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

## On the Closure Operator and the Closure System of Many Sorted Sets

Artur Kornilowicz
Institute of Mathematics, Warsaw University, Bialystok

### Summary.

In this paper definitions of many sorted closure system and many sorted closure operator are introduced. These notations are also introduced in [9], but in another meaning. In this article closure system is absolutely multiplicative subset family of many sorted sets and in [9] is many sorted absolutely multiplicative subset family of many sorted sets. Analogously, closure operator is function between many sorted sets and in [9] is many sorted function from a many sorted set into a many sorted set.

#### MML Identifier: CLOSURE2

The terminology and notation used in this paper have been introduced in the following articles [11] [5] [15] [10] [16] [2] [4] [3] [6] [12] [13] [14] [1] [8] [7]

#### Contents (PDF format)

1. Preliminaries
2. Set of Many Sorted Subsets of a Many Sorted Set
3. Many Sorted Operator corresponding to the Operator on Many Sorted Subsets
4. Properties of Closure Operators
5. On the Closure Operator and the Closure System

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