A topological characterization of the Sierpinski triangle

作者：Vejnar Benjamin^*

来源：Topology and Its Applications, 2012, 159(5): 1404-1408.

DOI：10.1016/j.topol.2011.12.019

• Continuum
• Sierpinski triangle
• Topological characterization

We present a topological characterization of the Sierpinski triangle. This answers question 58 from the Problem book of the Open Problem Seminar held at Charles University. In fact we give a characterization of the Apollonian gasket first. Consequently we show that any subcontinuum of the Apollonian gasket, whose boundary consists of three points, is homeomorphic to the Sierpinski triangle.

• 出版日期2012-3-15