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We generalize in a substantial way the celebrated result by Graham Higman, Bern-hard Neumann and Hanna Neumann on embedding countable groups into 2-generator groups as follows: every countable topological group is isomorphic to a topological subgroup of a topological group algebraically generated by two elements. A number of corollaries are derived. In particular, we characterize those topological groups embeddable into groups with two topological generators: they are the groups covered by countably many translations of each neighbourhood of the identity and having weight at most c. In particular, they include all sep-arable topological groups.