Definition:Divisor Topology
Jump to navigation
Jump to search
Definition
Let $S = \set {x \in \Z: x \ge 2}$ denote the set of integers greater than $1$.
Let $\BB$ be the set of all sets $U_n$ defined for all $n \ge 2$ as:
- $U_n = \set {x \in \Z_{>0}: x \divides n}$
where $\divides$ denotes the divisor relation.
Then $\BB$ is the basis for a topology $\tau$ on $S$.
Then $\tau$ is referred to as the divisor topology.
The topological space $T = \struct {S, \tau}$ is referred to as the divisor space.
Also see
- Results about the divisor topology can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (next): Part $\text {II}$: Counterexamples: $57$. Divisor Topology