Category:Smirnov's Deleted Sequence Topology
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This category contains results about Smirnov's Deleted Sequence Topology.
Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.
Let $A$ denote the set defined as:
- $A := \set {\dfrac 1 n: n \in \Z_{>0} }$
Let $\tau$ be the topology defined as:
- $\tau = \set {H: \exists U \in \tau_d, B \subseteq A: H = U \setminus B}$
That is, $\tau$ consists of the open sets of $\struct {\R, \tau_d}$ which have had any number of the set of the reciprocals of the positive integers removed.
$\tau$ is then referred to as Smirnov's deleted sequence topology on $\R$.
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