JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
Let X be a topological space, that is, a space
with open sets such that the union of any collection of open sets is open and the
intersection of any finite number of open sets is open. A covering of
X is a collection of open sets whose union is
X. The covering is called countable if it consists
of a countable collection of open sets or finite if it consists of a finite
collection of open sets ; it is called locally finite if every point of
X is contained in some open set which meets only a
finite number of sets of the covering. A covering is called a
refinement of a covering U if every open set of X is
contained in some open set of . The space
X is called countably paracompact if every countable
covering has a locally finite refinement.
Spaces and frames.The open sets of a topological space ~ form a complete lattice tX in which the join is the union, while the meet is the interior of the intersection:h~ny of the properties of a topological space X, e.g. tne properties of
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.