Displaying similar documents to “Introduction to Matroids”

The Vector Space of Subsets of a Set Based on Symmetric Difference

Jesse Alama (2008)

Formalized Mathematics

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For each set X, the power set of X forms a vector space over the field Z2 (the two-element field {0, 1} with addition and multiplication done modulo 2): vector addition is disjoint union, and scalar multiplication is defined by the two equations (1 · x:= x, 0 · x := ∅ for subsets x of X). See [10], Exercise 2.K, for more information.MML identifier: BSPACE, version: 7.8.05 4.89.993

Representing free Boolean algebras

Alan Dow, P. Nyikos (1992)

Fundamenta Mathematicae

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Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with 1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not...

Borel-Cantelli Lemma

Peter Jaeger (2011)

Formalized Mathematics

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This article is about the Borel-Cantelli Lemma in probability theory. Necessary definitions and theorems are given in [10] and [7].

A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-Páramo, Noé Trinidad Tapia-Bonilla (2007)

Commentationes Mathematicae Universitatis Carolinae

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The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If X is a T 2 -space, then | X | 2 L ( X ) χ ( X ) . Moreover, we will show relative versions of three well-known cardinal inequalities.