From the article:

> The three Laureates’ use of topological concepts in physics was decisive for their discoveries. Topology is a branch of mathematics that describes properties that only change step-wise.

I've never heard topology characterized that way. Typically I think of it as dealing with connection properties—sort of a more abstract geometry where objects can be considered the same even if their shape changes; identity is only defined by which parts are connected to which.

Could anyone elaborate on the 'step-wise' change aspect from the article?