Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes

James F. Peters

doi:10.33187/jmsm.425066

EN

Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes

Abstract

This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's smoke rings. A vortex cycle is a collection of non-concentric, nesting 1-cycles with nonempty interiors i.e., a collection of 1-cycles that share a nonempty set of interior points and which may or may not overlap). Overlapping 1-cycles in a vortex yield an Edelsbrunner-Harer nerve within the vortex. Overlapping vortex cycles constitute a vortex nerve complex. Several main results are given in this paper, namely, a Whitehead CW topology and a Leader uniform topology are outcomes of having a collection of vortex cycles (or nerves) equipped with a connectedness proximity and the case where each cluster of closed, convex vortex cycles and the union of the vortex cycles in the cluster have the same homotopy type.

Keywords

Connectedness Proximity, CW Topology, Vortex Cycle, Vortex Nerve, Vortex Nerve

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

James F. Peters ^*
Canada

Publication Date

September 30, 2018

Submission Date

May 18, 2018

Acceptance Date

July 17, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

DOI

https://doi.org/10.33187/jmsm.425066

IZ

https://izlik.org/JA46ZW39HY

APA

Peters, J. F. (2018). Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling, 1(2), 56-72. https://doi.org/10.33187/jmsm.425066

AMA

1.Peters JF. Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling. 2018;1(2):56-72. doi:10.33187/jmsm.425066

Chicago

Peters, James F. 2018. “Proximal Vortex Cycles and Vortex Nerve Structures. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes”. Journal of Mathematical Sciences and Modelling 1 (2): 56-72. https://doi.org/10.33187/jmsm.425066.

EndNote

Peters JF (September 1, 2018) Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling 1 2 56–72.

IEEE

[1]J. F. Peters, “Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 2, pp. 56–72, Sept. 2018, doi: 10.33187/jmsm.425066.

ISNAD

Peters, James F. “Proximal Vortex Cycles and Vortex Nerve Structures. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes”. Journal of Mathematical Sciences and Modelling 1/2 (September 1, 2018): 56-72. https://doi.org/10.33187/jmsm.425066.

JAMA

1.Peters JF. Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling. 2018;1:56–72.

MLA

Peters, James F. “Proximal Vortex Cycles and Vortex Nerve Structures. Non-Concentric, Nesting, Possibly Overlapping Homology Cell Complexes”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 2, Sept. 2018, pp. 56-72, doi:10.33187/jmsm.425066.

Vancouver

1.James F. Peters. Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling. 2018 Sep. 1;1(2):56-72. doi:10.33187/jmsm.425066