# Understanding Sierpinski carpet formally

In this paper, one definition of carpet(Sierpinski) is given as follows: A metrizable topological space is a carpet iff it is a planar continuum of topological dimension 1 that is locally connected and has no local cut points.

I don't quite understand the use of locally connectedness in my intuitive understanding of the Sierpinski carpet as a fractal. What would the geometric structure look like in the absence of locally connected property? Any suggestions?