PARSED CONTENT

The site had the following in the homepage, "Baire category theorem and applications." I noticed that the web site stated " Is a topological space for which the intersection of every countable collection of dense open sets is dense." They also stated " The next result due to René-Louis Baire asserts that complete metric spaces are Baire spaces. The proof of this result heavily depends on the axiom of dependent choice, and in fact, they are equivalent under ZF, as we shall see later. Every complete metric space is a Baire space. Be a complete metric space with distance."