Finding Connected Components

Topology · Axiom Academy

EXAMPLE Finding Connected Components Step-by-step decomposition of spaces into their connected pieces Connected Components of the Rationals Test if any subset is connected has infinitely many connected components Every point is isolated in the component topology Connected Components of a Discrete Space Show each interval is connected Show intervals cannot be joined You've seen three important examples of finding connected components: 1. Totally disconnected spaces (rationals) 2. Discrete spaces (every point separate) 3. Unions of intervals (each piece is a component) Based on the example above, which approach is correct?

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