Definition:Evenly Spaced Integer Topology
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Definition
Let $\Z$ denote the set of integers.
Let $\BB$ be the set of sets defined as:
- $\BB = \set {a + k \Z: a, k \in \Z, k \ne 0}$
where $a + k \Z := \set {a + k \lambda: \lambda \in \Z}$.
Then $\BB$ is the basis for a topology $\tau$ on $S$.
Then $\tau$ is referred to as the evenly spaced integer topology.
The topological space $T = \struct {S, \tau}$ is referred to as the evenly spaced integer space.
Also see
- Results about the evenly spaced integer 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: $58$. Evenly Spaced Integer Topology