Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

## Sequences of Metric Spaces and an Abstract Intermediate Value Theorem

Yatsuka Nakamura
Shinshu University, Nagano
Andrzej Trybulec
University of Bialystok

### Summary.

Relations of convergence of real sequences and convergence of metric spaces are investigated. An abstract intermediate value theorem for two closed sets in the range is presented. At the end, it is proven that an arc connecting the west minimal point and the east maximal point in a simple closed curve must be identical to the upper arc or lower arc of the closed curve.

This work has been partially supported by the European Community TYPES grant IST-1999-29001 and CALCULEMUS grant HPRN-CT-2000-00102.

#### MML Identifier: TOPMETR3

The terminology and notation used in this paper have been introduced in the following articles [22] [24] [1] [23] [25] [4] [5] [3] [13] [19] [7] [2] [21] [8] [6] [9] [17] [15] [14] [16] [12] [20] [18] [10] [11]

Contents (PDF format)

#### Bibliography

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Received September 11, 2002

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