Can You Walk There?

Topology · Axiom Academy

An intuitive introduction to path connectedness in topology Imagine you're standing at point A in some space. You want to get to point B. The question seems simple: Can you walk there? Not by teleporting, not by jumping through space—but by taking a continuous path , never lifting your pencil, never breaking the connection. Here's a circle. Click anywhere on the circle to place two points, then watch as we draw a path between them. Can we always walk from one point to another? Now we have two circles that don't touch. Try placing one point on each circle. Can we walk between them? Let's look at several spaces and their "walkability." Some are path-connected, others are not.

This is the written version of the interactive lesson above. See the full Topology course.