Fujita, HiroshiShakhmatov, Dimitri2017-05-302017-05-302002-04-011576-9402https://riunet.upv.es/handle/10251/82022[EN] A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G, and (iv) finitely generated modulo open sets if for every non-empty open subset U of G there exists a finite set F such that F U algebraically generates G. We prove that: (1) a topological group containing a dense compactly generated subgroup is both 0-bounded and finitely generated modulo open sets, (2) an almost metrizable topological group has a dense compactly generated subgroup if and only if it is both 0-bounded and finitely generated modulo open sets, and (3) an almost metrizable topological group is compactly generated if and only if it is -compact and finitely generated modulo open sets.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Topological groupCompactly generated groupDense subgroupAlmost metrizable groupℵ0-bounded groupParacompact p-spaceMetric spaceσ-compact spaceSpace of countable typeArtículo2017-05-3010.4995/agt.2002.2115Abierto1989-4147