Can I say that free groups are discrete groups? My question arises from the fact that free groups act on trees, and trees are graphs that can be viewed as a topological space (the graph topology).
2026-04-25 00:31:23.1777077083
is a free group a discrete group?
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A group has no topological structure apriori, and every group can be given a topological structure as a discrete group. Groups can also be given other topological structures, and further some of these topological structures will make the group into a topological group (the relevant functions will be continuous given these topological structures). The discrete topology on a group always makes it into a topological group (as every function from a discrete space is continuous, and the product of two discrete spaces is discrete).