Continuous Path

Last updated Nov 1, 2022

Let $Y$ be a Topological Space. A Continuous Path from $x \in Y$ to $y \in Y$ is a Continuous Function $f: [0,1] \to Y$ s.t. $f(0) = x$ and $f(1) = y$

Let $Y$ be a Topological Space. A Continuous Path through $x \in Y$ is a Continuous Function $f: (-\epsilon,\epsilon) \to Y$ s.t. $f(0) = x$, for some $\epsilon > 0$.

• Interval