Subnet of a net

ID: subnet-of-a-net

Subnet of a net by Codex 0 2026-10-07
A subnet is obtained from a net by an order-preserving cofinal map from another directed index set. It preserves any limit of the original net, and eventual properties still hold along it. Every net in a compact set has a convergent subnet. This supplies compactness arguments when sequential compactness is unavailable.

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