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

## Intermediate Value Theorem and Thickness of Simple Closed Curves

Yatsuka Nakamura
Shinshu University, Nagano
Andrzej Trybulec
University of Bialystok

### Summary.

Various types of the intermediate value theorem ( [14]) are proved. For their special cases, the Bolzano theorem is also proved. Using such a theorem, it is shown that if a curve is a simple closed curve, then it is not horizontally degenerated, neither is it vertically degenerated.

#### MML Identifier: TOPREAL5

The terminology and notation used in this paper have been introduced in the following articles [15] [18] [1] [17] [19] [4] [12] [6] [13] [2] [10] [3] [7] [8] [9] [11] [16] [5]

#### Contents (PDF format)

1. Intermediate Value Theorems and Bolzano Theorem
2. Simple Closed Curves Are Not Flat

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