- 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...
- 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...
- 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...
-
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...
- {\displaystyle \mathbb {1} _{S}} is com****ble. Examples:
Every finite or
cofinite subset of the
natural numbers is com****ble. This
includes these special...
- 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...
- 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...
-
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...
-
weakly countably compact nor
countably metacompact,
hence not compact.
Cofinite topology List of
topologies Steen, Lynn Arthur; Seebach, J.
Arthur Jr....
