Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

Compactness of the Bounded Closed Subsets of $\cal E^2_\rm T$


Artur Kornilowicz
University of Bialystok
This paper was written while the author visited Shinshu University, winter 1999.

Summary.

This paper contains theorems which describe the correspondence between topological properties of real numbers subsets introduced in [35] and introduced in [33], [14]. We also show the homeomorphism between the cartesian product of two $R^1$ and ${\cal E}^2_{\rm T}$. The compactness of the bounded closed subset of ${\cal E}^2_{\rm T}$ is proven.

MML Identifier: TOPREAL6

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

Contents (PDF format)

  1. Real Numbers
  2. Topological Preliminaries
  3. Points and Subsets in ${\cal E}^2_{\rm T}$
  4. Balls as subsets of ${\cal E}^n_{\rm T}$
  5. Topological Properties of Real Numbers Subsets
  6. Bounded Subsets

Acknowledgments

I would like to thank Professor Yatsuka Nakamura for his help in the preparation of the article.

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Received February 19, 1999


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