Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## Introduction to the Homotopy Theory

University of Bialystok

### Summary.

The paper introduces some preliminary notions concerning the homotopy theory according to [15]: paths and arcwise connected to topological spaces. The basic operations on paths (addition and reversing) are defined. In the last section the predicate: $P, Q$ {\em are homotopic} is defined. We also showed some properties of the product of two topological spaces needed to prove reflexivity and symmetry of the above predicate.

#### MML Identifier: BORSUK_2

The terminology and notation used in this paper have been introduced in the following articles [20] [10] [22] [16] [23] [7] [9] [8] [19] [13] [4] [1] [12] [18] [11] [17] [21] [24] [14] [6] [5] [2] [3]

#### Contents (PDF format)

1. Preliminaries
2. Paths and arcwise connected spaces
3. Basic operations on paths
4. The product of two topological spaces

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