11. By applying Pontryagin duality, one can see that abelian profinite groups are in duality with locally finite discrete abelian groups. 12. If a collection of sets is locally finite , the collection of all closures of these sets is also locally finite. 13. If a collection of sets is locally finite, the collection of all closures of these sets is also locally finite . 14. A ?-locally finite base is a base which is a union of countably many locally finite collections of open sets. 15. A ?-locally finite base is a base which is a union of countably many locally finite collections of open sets. 16. For example, a poset is "'locally finite "'if every closed Euler characteristic of finite bounded posets. 17. For graphs that may not be locally finite , it is still possible to define a topological space from the graph and its ends. 18. It states that a topological space is metrizable if and only if it is regular, Hausdorff and has a ?-locally finite base. 19. *PM : uniformly locally finite graph, id = 8050 new !-- WP guess : uniformly locally finite graph-- Status: 20. *PM : uniformly locally finite graph, id = 8050 new !-- WP guess : uniformly locally finite graph-- Status:
