User:Leigh.Samphier/Topology/Completed

Summation
Definition:Summation over Finite Subset

Summation over Finite Subset is Well-Defined

Definition:Summation over Finite Index

Summation over Finite Index is Well-Defined

Summation over Union of Disjoint Finite Index Sets

Generalized Sum
Finite Generalized Sum Converges to Summation

Generalized Sum Restricted to Non-zero Summands

Corollary of Generalized Sum Restricted to Non-zero Summands

Generalized Sum with Finite Non-zero Summands

Absolute Net Convergence Equivalent to Absolute Convergence

Generalized Sum of Constant Zero Converges to Zero

Generalized Sum with Countable Non-zero Summands

Corollary of Generalized Sum with Countable Non-zero Summands

Generalized Hilbert Sequence Space
Definition:Generalized Hilbert Sequence Space

Characterization of Generalized Hilbert Sequence Space

Generalized Hilbert Sequence Space is Metric Space

Other
Restriction of Restriction is Restriction

Countably Infinite Set has Enumeration