How to avoid a loop in R: selecting items from a list

I could solve this using loops, but I am trying think in vectors so my code will be more R-esque.

I have a list of names. The format is firstname_lastname. I want to get out of this list a separate list with only the first names. I can't seem to get my mind around how to do this. Here's some example data:

t <- c("bob_smith","mary_jane","jose_chung","michael_marx","charlie_ivan")
tsplit <- strsplit(t,"_")

which looks like this:

> tsplit
[[1]]
[1] "bob"   "smith"

[[2]]
[1] "mary" "jane"

[[3]]
[1] "jose"  "chung"

[[4]]
[1] "michael" "marx"   

[[5]]
[1] "charlie" "ivan"   

I could get out what I want using loops like this:

for (i in 1:length(tsplit)){
    if (i==1) {t_out <- tsplit[[i]][1]} else{t_out <- append(t_out, tsplit[[i]][1])} 
}

which would give me this:

t_out
[1] "bob"     "mary"    "jose"    "michael" "charlie"

So how can I do this without loops?