locally finite collection

Let $𝒞$ be a collection of subsets of a topological space $X$.

$𝒞$ is said to be locally finite if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U\cap A=\mathrm{\varnothing }$ for all but finitely many $A\in 𝒞$.

Similarly, $𝒞$ is said to be locally countable if for all $x\in X$ there is a neighbourhood $U$ of $x$ such that $U\cap A=\mathrm{\varnothing }$ for all but countably many $A\in 𝒞$.

Title	locally finite collection
Canonical name	LocallyFiniteCollection
Date of creation	2013-03-22 12:12:51
Last modified on	2013-03-22 12:12:51
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	11
Author	yark (2760)
Entry type	Definition
Classification	msc 54D20
Related topic	PointFinite
Defines	locally finite
Defines	locally countable collection
Defines	locally countable