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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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Union of Two Faces, using the Jordan Curve Theorem

Consider four disjoint points in the plane, $v_{1}$, $v_{2}$, $v_{3}$ and $v_{4}$. The cycle, $C:=v_1v_2v_{3}v_{4}v_{1}$, is the union of the (Jordan) arcs, $A_{12}$, $A_{23}$, $A_{34}$, and $A_{41}$, …