Category:Either-Or Topology

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This category contains results about Either-Or Topology.

Let $S = \closedint {-1} 1$ be the closed interval on the real number line from $-1$ to $1$.

Let $\tau \subseteq \powerset S$ be a subset of the power set of $S$ such that, for any $H \subseteq S$:

$H \in \tau \iff \paren {\set 0 \nsubseteq H \lor \openint {-1} 1 \subseteq H}$

where $\lor$ is the inclusive-or logical connective.

Then $\tau$ is the either-or topology, and $T = \struct {S, \tau}$ is the either-or space