The Koch curve as a smooth manifold. (English) Zbl 1146.28300

Summary: We show that there exists a homeomorphism between the closed interval \([0,1]\subset \mathbb R\) and the Koch curve endowed with the subset topology of \(\mathbb R\). We use this homeomorphism to endow the Koch curve with the structure of a smooth manifold with boundary.


28A80 Fractals
57R99 Differential topology
Full Text: DOI


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