Definition:Odd-Even Topology

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Definition

Let $\Z_{>0}$ denote the set of strictly positive integers:

$\Z_{>0} = \set {x \in \Z: x > 0}$


Let $\PP$ be the partition on $\Z_{>0}$ defined as:

$\PP = \set {\set {2 k - 1, 2 k}: k \in \Z_{>0} }$

That is:

$\PP = \set {\set {1, 2}, \set {3, 4}, \set {5, 6}, \ldots}$


Then the topology whose basis is $\PP$ is called the odd-even topology.


Also see

  • Results about the odd-even topology can be found here.


Sources