- In mathematics, a
cofinite subset of a set X {\displaystyle X} is a
subset A {\displaystyle A}
whose complement in X {\displaystyle X} is a
finite set...
- In mathematics, the Fréchet filter, also
called the
cofinite filter, on a set X {\displaystyle X} is a
certain collection of
subsets of X {\displaystyle...
-
topology Cocountable topology Cofinite topology Compact-open
topology Compactification Discrete topology Double-pointed
cofinite topology Extended real number...
- of all the open sets
containing it.
Every finite set is closed.
Every cofinite set of X {\displaystyle X} is open. For
every x ∈ X , {\displaystyle x\in...
- a
cofinite set with any set is
cofinite,
while the
union of two
finite sets is finite.
Intersection behaves like
union with "finite" and "
cofinite" interchanged...
-
Hausdorff spaces where limit points are unique. Any set can be
given the
cofinite topology in
which the open sets are the
empty set and the sets
whose complement...
-
Toronto spaces, namely: the
discrete topology, the
indiscrete topology, the
cofinite topology and the
upper and
lower topologies on the
natural numbers. The...
-
finite or
cofinite is a
Boolean algebra and an
algebra of sets
called the finite–
cofinite algebra. If S is
infinite then the set of all
cofinite subsets...
- A
simple example of a
topology that is T1 but is not
Hausdorff is the
cofinite topology defined on an
infinite set, as is the
cocountable topology defined...
-
cocountable subset of the reals. If the
complement is finite, then one says Y is
cofinite. The set of all
subsets of X that are
either countable or
cocountable forms...
