Topology of slices through the Sierpiński tetrahedron

Yuto Nakajima and Takayuki Watanabe

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each c∈[0,1], we study the Čech (co)homology group of the slice at height c. We show that the topology of the slice exhibits a sharp dichotomy. If c is a dyadic rational, then the slice has finitely many connected components, infinite first Čech homology, and trivial higher homology. If c is not a dyadic rational, then the slice is totally disconnected and all positive-degree Čech homology groups vanish.

Keywords: Fractal; Čech homology; Iterated function systems; Connectedness; Slices of fractals; Fractal dimensions (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077926004947
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926004947

DOI: 10.1016/j.chaos.2026.118353

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().