Homeomorphism between [:$\cal E^i_\rm T, \cal E^j_\rm T$:] and $\cal E^i+j_\rm T$

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

Homeomorphism between [:$\cal E^i_\rm T, \cal E^j_\rm T$:] and $\cal E^i+j_\rm T$

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

Summary.

In this paper we introduce the cartesian product of two metric spaces. As the distance between two points in the product we take maximal distance between coordinates of these points. In the main theorem we show the homeomorphism between [:${\cal E}^i_{\rm T}, {\cal E}^j_{\rm T}$:] and ${\cal E}^{i+j}_{\rm T}$.

MML Identifier: TOPREAL7

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

Contents (PDF format)

Acknowledgments

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

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.

[3] Leszek Borys. Paracompact and metrizable spaces. Journal of Formalized Mathematics, 3, 1991.

[4] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[5] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[6] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[7] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[8] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.

[9] Czeslaw Bylinski. The sum and product of finite sequences of real numbers. Journal of Formalized Mathematics, 2, 1990.

[10] Agata Darmochwal. The Euclidean space. Journal of Formalized Mathematics, 3, 1991.

[11] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[12] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.

[13] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[14] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[15] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[16] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[17] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.

[18] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[19] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.

[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[21] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[22] Mariusz Zynel and Adam Guzowski. \Tzero\ topological spaces. Journal of Formalized Mathematics, 6, 1994.

Received February 21, 1999

[ Download a postscript version, MML identifier index, Mizar home page]