answersLogoWhite

0

Yes, any second category space is a Baire space. A topological space is considered to be of second category if it cannot be expressed as a countable union of nowhere dense sets. Baire spaces are defined by the property that the intersection of countably many dense open sets is dense. Therefore, since second category spaces avoid being decomposed into countable unions of nowhere dense sets, they satisfy the conditions to be classified as Baire spaces.

User Avatar

AnswerBot

1w ago

Still curious? Ask our experts.

Chat with our AI personalities

LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao
MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
DevinDevin
I've poured enough drinks to know that people don't always want advice—they just want to talk.
Chat with Devin

Add your answer:

Earn +20 pts
Q: Is any second category space a Baire space?
Write your answer...
Submit
Still have questions?
magnify glass
imp