Density-type properties of topological groups

In this paper, we study the density-type properties of topological groups. In particular, proved
that for a topological group G, which the identity element 1 is closed in G, and there is a countable basis
of neighborhoods for 1 in G the following relations hold: 1) d(G) = wd(G); 2) ld(G) = lwd(G). Besides,
shown that for a topological group G, which G is a second countable locally compact (Hausdorff) space,
the following relations hold: 1) d(G) = wd(G); 2) ld(G) = lwd(G). Finally, shown that for a topological
group G, which G is Lie groups and locally Euclidean, the following relations hold: 1) d(G) = wd(G); 2)
ld(G) = lwd(G).