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

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

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