Category:Arc Components

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This category contains results about Arc Components.

Let $T$ be a topological space.

Let us define the relation $\sim$ on $T$ as follows:

$x \sim y \iff x$ and $y$ are arc-connected.


We have that $\sim $ is an equivalence relation, so from the Fundamental Theorem on Equivalence Relations, the points in $T$ can be partitioned into equivalence classes.

These equivalence classes are called the arc components of $T$.

Pages in category "Arc Components"

The following 2 pages are in this category, out of 2 total.