The Baire category theorem (BCT) is an important result in general topology and functional analysis.

1 We shall then apply the Baire category theorem to prove three fundamental results in functional analysis: the Uniform Boundedness Theorem, the Open Mapping ...

A result in analysis and set theory which roughly states that in certain spaces, the intersection of any countable collection of large sets remains large.

The Baire category theorem then states that a complete metric space X is not meagre. Continuous, nowhere differentiable functions. We now give the classic.

8 июн. 2009 г. · We present five versions of this theorem and give proof of their equivalence. (1) Every interval [a,b] is a set of the second category.

31 янв. 1997 г. · Theorem 2 (Baire Category Theorem) A complete metric space cannot be expressed as a countable union of nowhere dense subsets. Definition 3 A ...

7 мар. 2013 г. · A topological space X is said to be a Baire space if every countable union of nowhere-dense subsets of X has empty interior. Definitions of Baire first and second category sets What is the intuition behind the terminology surrounding Baire's ... Equivalence of Baire Category Theorem for Complete Metric ... Your favourite application of the Baire Category Theorem Другие результаты с сайта math.stackexchange.com

13 янв. 2018 г. · This short note is devoted to a simple proof of the Baire Category Theorem for topological spaces that are homeomorphic to complete metric ...

1 февр. 2009 г. · The Baire category theorem is equivalent to the claim that in a complete metric space, the countable intersection of open dense sets remain dense.

By Baire category, not all En's are nowhere dense. Hence En = En must contain a non-empty open set U for some n. Take C = n. Theorem 6. .