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This category contains definitions related to Convergence.
Related results can be found in Category:Convergence.

Let $T = \struct {S, \tau}$ be a topological space.

Let $A \subseteq S$.

Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence in $A$.

Then $\sequence {x_n}$ converges to the limit $\alpha \in S$ if and only if:

$\forall U \in \tau: \alpha \in U \implies \paren {\exists N \in \R_{>0}: \forall n \in \N: n > N \implies x_n \in U}$

Pages in category "Definitions/Convergence"

The following 72 pages are in this category, out of 72 total.