### Some articles on *cofinite*:

**Cofinite**ness -

**Cofinite**Topology - Double-pointed

**Cofinite**Topology

... The double-pointed

**cofinite**topology is the

**cofinite**topology with every point doubled that is, it is the topological product of the

**cofinite**topology with the indiscrete topology ... An example of a countable double-pointed

**cofinite**topology is the set of even and odd integers, with a topology that groups them together ...

**Cofinite**ness -

**Cofinite**Topology

... The

**cofinite**topology (sometimes called the finite complement topology) is a topology which can be defined on every set X ... It has precisely the empty set and all

**cofinite**subsets of X as open sets ... As a consequence, in the

**cofinite**topology, the only closed subsets are finite sets, or the whole of X ...

Fréchet Filter

... In mathematics, the Fréchet filter, also called the

... In mathematics, the Fréchet filter, also called the

**cofinite**filter, on a set is a special subset of the set's power set ... It is alternatively called a**cofinite**filter because its members are exactly the**cofinite**sets in a power set ...**Cofinite**ness -

**Cofinite**Topology - Properties

... Subspaces Every subspace topology of the

**cofinite**topology is also a

**cofinite**topology ... Separation The

**cofinite**topology is the coarsest topology satisfying the T1 axiom i.e ... an arbitrary topology on X satisfies the T1 axiom if and only if it contains the

**cofinite**topology ...

T

... The

_{1}Space - Examples... The

**cofinite**topology on an infinite set is a simple example of a topology that is T1 but is not Hausdorff (T2) ... This follows since no two open sets of the**cofinite**topology are disjoint ... modified slightly to create the double-pointed**cofinite**topology, which is an example of an R0 space that is neither T1 nor R1 ...Main Site Subjects

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