Category:Limits of Sequence of Sets

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This category contains results about Limits of Sequence of Sets.

Let $\struct {X, \tau}$ be a Hausdorff topological space.

Let $\sequence {C_n}_{n \mathop \in \N}$ be a sequence of sets in $X$.

The inner limit of $\sequence {C_n}_{n \mathop \in \N}$ is defined as:

$\ds \liminf_{n \mathop \to \infty} \ C_n := \set {x \in X: \exists N \text{ cofinite set of } \N, \exists x_v \in C_v \paren {v \in N} \text{ such that } x_v \to x}$

where $x_v \to x$ denotes convergence in the topology $\tau$.

The pages listed here refer to results on inner and outer limits of sequences of sets in Hausdorff topological spaces.