Quelques notes sur l’acteur-danseur dans le théâtre de Jan Fabre

Hilbert’s fifth problem for local groups

“…In the rest of this section, we assume that G is NSS and that U is a special neighborhood of 1 in G. We now lead up to the proof of the crucial fact that the image of the local exponential map is a neighborhood of 1 in G. In particular, we will see that there is an open neighborhood of 1 in G which is ruled by local 1-parameter subgroups in the sense that every element in this open neighborhood lies on some local 1-ps of G. In the rest of this section, we do not follow [6], but rather [3], which contains the following series of lemmas in the global setting.…”

“…Definition 2. 3. A subgroup of G is a subset H ⊆ G such that 1 ∈ H, H ⊆ Λ, H × H ⊆ Ω and for all x, y ∈ H, x −1 ∈ H and xy ∈ H.…”