Pathwise Connected
# Definition
Let $(X, \tau)$ be a Topological Space. We say that $X$ is Path-Connected if for every $x, y \in X$, there exists a Continuous Function $f: [0,1] \to X$ so that $f(0) = x$ and $f(1) = y$
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Let $(X, \tau)$ be a Topological Space. We say that $X$ is Path-Connected if for every $x, y \in X$, there exists a Continuous Function $f: [0,1] \to X$ so that $f(0) = x$ and $f(1) = y$