Definition:Interlocking Interval Topology
Jump to navigation
Jump to search
Definition
Let $S = \R_{>0} \setminus \Z_{>0}$ denote the set of (strictly) positive real numbers excluding the positive integers.
Let $\BB$ be the family of sets $\family {S_n}_{n \mathop \in \Z_{>0} }$ defined as:
- $S_n = \set {\openint 0 {\dfrac 1 n} \cup \openint n {n + 1} }$
Then $\BB$ is the basis for a topology $\tau$ on $S$.
$\tau$ is referred to as the interlocking interval topology.
The topological space $T = \struct {S, \tau}$ is referred to as the interlocking interval space.
Also see
- Results about the interlocking interval 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: $54$. Interlocking Interval Topology