Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

More on External Approximation of a Continuum

Andrzej Trybulec
University of Bialystok

Summary.

The main goal was to prove two facts: \begin{itemize} \itemsep-3pt \item the gauge is the Go-Board of a corresponding cage, \item the left components of the complement of the curve determined by a cage are monotonic wrt the index of the approximation. \end{itemize} Some auxiliary facts are proved, too. At the end the new notion needed for the internal approximation are defined and some useful lemmas are proved.

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

MML Identifier: JORDAN1H

The terminology and notation used in this paper have been introduced in the following articles [37] [10] [46] [39] [12] [32] [3] [40] [22] [2] [42] [34] [47] [49] [48] [7] [9] [8] [1] [4] [19] [5] [11] [44] [13] [23] [24] [43] [45] [28] [36] [50] [18] [35] [6] [20] [30] [41] [21] [26] [27] [31] [33] [29] [16] [38] [14] [15] [17] [25]

Contents (PDF format)

1. Preliminaries
2. Transforming Finite Sets to Finite Sequences
3. On the Construction of Go-Boards
7. Preparing the Internal Approximation

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