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[itex]S0_O(3,1) = \{ a \in SO(3,1) | (ae_4,e_4) < 0 \}[/itex]

i need to show this group is connected

in my notes it says a group G is connected if it satisfies any of the following:

(i)any two elements of G can be joined by a [itex]C^k[/itex]-path in G

(ii) it is not the disjoint union of two non-empty open sets

(iii) it is generated by a neighbourhood of 1 (the identity matrix)

(iv) it is generated by [itex]exp \mathfrak{g}[/itex]

im not sure which one to try and prove or how to go about it really. can anybody offer some advice? thanks.

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# Homework Help: SO(3,1) Connectedness problem

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