Definition:Deleted Integer Topology
Jump to navigation
Jump to search
Definition
Let $\PP$ be the set:
- $\PP = \set {\openint {n - 1} n: n \in \Z_{> 0} }$
that is, the set of all open real intervals of the form:
- $\openint 0 1, \openint 1 2, \openint 2 3, \ldots$
Let $S$ be the set defined as:
- $S = \ds \bigcup \PP = \R_{\ge 0} \setminus \Z$
that is, the positive real numbers minus the integers.
Let $T = \struct {S, \tau}$ be the partition topology whose basis is $\PP$.
Then $T$ is called the deleted integer topology.
Also see
- Results about the deleted integer topology can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $7$. Deleted Integer Topology: $5$