Category:Definitions/Convergence

From ProofWiki
Jump to navigation Jump to search

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


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

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

Subcategories

This category has the following 8 subcategories, out of 8 total.

Pages in category "Definitions/Convergence"

The following 66 pages are in this category, out of 66 total.

C