Topic: Neighborhoods, Limit Points and Convergence

Tails, Subsequences, and Eventual Properties

Subnets and Cluster Points of Nets

Sequence-And-Net Diagnostic Problems

Nonunique Sequence Limits in Non-Hausdorff Spaces

Nets Detect Closure in Every Topological Space

Neighborhoods of a Point

Neighborhood Systems and Their Axioms

Neighborhood Bases and Open Neighborhoods

Local Bases and First Countability

Limit-Point Calculations in Familiar Topologies