Jump to ContentJump to Main Navigation
Show Summary Details

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2015: 0.134
Source Normalized Impact per Paper (SNIP) 2015: 0.686
Impact per Publication (IPP) 2015: 0.296

Open Access
Online
ISSN
1898-9934
See all formats and pricing
Volume 17, Issue 3 (Jan 2009)

Issues

Small Inductive Dimension of Topological Spaces

Karol Pąk
  • Institute of Computer Science, University of Białystok, Poland
Published Online: 2010-07-08 | DOI: https://doi.org/10.2478/v10037-009-0025-7

Small Inductive Dimension of Topological Spaces

We present the concept and basic properties of the Menger-Urysohn small inductive dimension of topological spaces according to the books [7]. Namely, the paper includes the formalization of main theorems from Sections 1.1 and 1.2.

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

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

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

  • [4] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

  • [5] Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.

  • [6] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

  • [7] Roman Duda. Wprowadzenie do topologii. PWN, 1986.

  • [8] Adam Grabowski. Properties of the product of compact topological spaces. Formalized Mathematics, 8(1):55-59, 1999.

  • [9] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

  • [10] Robert Milewski. Bases of continuous lattices. Formalized Mathematics, 7(2):285-294, 1998.

  • [11] Andrzej Nędzusiak. s-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.

  • [12] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

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

  • [14] Karol Pąk. Basic properties of metrizable topological spaces. Formalized Mathematics, 17(3):201-205, 2009, doi: 10.2478/v10037-009-0024-8. [Crossref]

  • [15] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.

  • [16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.

  • [17] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.

  • [18] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.

  • [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

  • [20] Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.

About the article


Published Online: 2010-07-08

Published in Print: 2009-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-009-0025-7. Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Karol Pąk
Formalized Mathematics, 2011, Volume 19, Number 3
[2]
Karol Pąk
Formalized Mathematics, 2009, Volume 17, Number 3

Comments (0)

Please log in or register to comment.
Log in