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This article introduces proximal planar vortex 1-cycles, resembling thestructure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867and recent work on the proximity of sets that overlap either spatially ordescriptively. Vortex cycles resemble Thomson's model of a vortex atom,inspired by P.G. Tait's smoke rings. A vortex cycle is a collection ofnon-concentric, nesting 1-cycles with nonempty interiors (i.e., a collection of1-cycles that share a nonempty set of interior points and which may or may notoverlap). Overlapping 1-cycles in a vortex yield an Edelsbrunner-Harer nervewithin the vortex. Overlapping vortex cycles constitute a vortex nerve complex.Several main results are given in this paper, namely, a Whitehead CW topologyand a Leader uniform topology are outcomes of having a collection of vortexcycles (or nerves) equipped with a connectedness proximity and the case whereeach cluster of closed, convex vortex cycles and the union of the vortex cyclesin the cluster have the same homotopy type.

Proximal Vortex Cycles and Vortex Nerves. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes