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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Online
ISSN
1898-9934
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Volume 18, Issue 3 (Jan 2010)

Issues

Miscellaneous Facts about Open Functions and Continuous Functions

Artur Korniłowicz
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0019-5

Miscellaneous Facts about Open Functions and Continuous Functions

In this article we give definitions of open functions and continuous functions formulated in terms of "balls" of given topological spaces.

  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Google Scholar

  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [3] Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.Google Scholar

  • [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [6] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Google Scholar

  • [7] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.Google Scholar

  • [8] Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.Google Scholar

  • [9] Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in ϵn/T. Formalized Mathematics, 12(3):301-306, 2004.Google Scholar

  • [10] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Google Scholar

  • [11] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Google Scholar

  • [12] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

  • [13] Mariusz Żynel and Adam Guzowski. T0 topological spaces. Formalized Mathematics, 5(1):75-77, 1996.Google Scholar

About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0019-5.

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