Definition:Integer Reciprocal Space
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Definition
Let $\struct {\R, \tau_d}$ be the real number line $\R$ under the usual (Euclidean) topology $\tau_d$.
Let $A \subseteq \R$ be the set of all points on $\R$ defined as:
- $A := \set {\dfrac 1 n : n \in \Z_{>0} }$
That is:
- $A := \set {1, \dfrac 1 2, \dfrac 1 3, \dfrac 1 4, \ldots}$
Then $\struct {A, \tau_d}$ is the integer reciprocal space.
Also see
- Results about the integer reciprocal space 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: $32$. Special Subsets of the Real Line: $1$