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

Some Properties of Dyadic Numbers and Intervals


Jozef Bialas
Lodz University
Yatsuka Nakamura
Shinshu University, Nagano

Summary.

The article is the second part of a paper proving the fundamental Urysohn Theorem concerning the existence of a real valued continuous function on a normal topological space. The paper is divided into two parts. In the first part, we introduce some definitions and theorems concerning properties of intervals; in the second we prove some of properties of dyadic numbers used in proving Urysohn Lemma.

MML Identifier: URYSOHN2

The terminology and notation used in this paper have been introduced in the following articles [11] [13] [1] [8] [12] [9] [2] [3] [4] [5] [6] [10] [7]

Contents (PDF format)

Bibliography

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[5] Jozef Bialas. Some properties of the intervals. Journal of Formalized Mathematics, 6, 1994.
[6] Jozef Bialas and Yatsuka Nakamura. Dyadic numbers and T$_4$ topological spaces. Journal of Formalized Mathematics, 7, 1995.
[7] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Journal of Formalized Mathematics, 11, 1999.
[8] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[9] Rafal Kwiatek. Factorial and Newton coefficients. Journal of Formalized Mathematics, 2, 1990.
[10] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.
[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[12] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[13] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received February 16, 2001


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