Definition:Integer Reciprocal Space

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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.