Complex sentence: This is, however, a phenomenon of finite dimensions: that all norms will turn out to be equivalent: they stay within constant multiples of each other, and from a topological point of view they give the same open sets.
Split into simpler sentences: This is, however, a phenomenon of finite dimensions. That all norms will turn out to be equivalent: they stay within constant multiples of each other, and from a topological point of view they give the same open sets.