Small Inductive Dimension of Topological Spaces

Pąk, Karol

doi:10.2478/v10037-009-0025-7

Abstract

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.

References

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
Search in Google Scholar
[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
Search in Google Scholar
[3] Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.
Search in Google Scholar
[4] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
[5] Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
Search in Google Scholar
[6] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
Search in Google Scholar
[7] Roman Duda. Wprowadzenie do topologii. PWN, 1986.
Search in Google Scholar
[8] Adam Grabowski. Properties of the product of compact topological spaces. Formalized Mathematics, 8(1):55-59, 1999.
Search in Google Scholar
[9] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
Search in Google Scholar
[10] Robert Milewski. Bases of continuous lattices. Formalized Mathematics, 7(2):285-294, 1998.
Search in Google Scholar
[11] Andrzej Nędzusiak. s-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.
Search in Google Scholar
[12] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
Search in Google Scholar
[13] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
Search in Google Scholar
[14] Karol Pąk. Basic properties of metrizable topological spaces. Formalized Mathematics, 17(3):201-205, 2009, doi: 10.2478/v10037-009-0024-8.10.2478/v10037-009-0024-8
Search in Google Scholar
[15] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.
Search in Google Scholar
[16] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
Search in Google Scholar
[17] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
Search in Google Scholar
[18] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
Search in Google Scholar
[19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
[20] Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.
Search in Google Scholar

Small Inductive Dimension of Topological Spaces

Abstract

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