I don't understand what's the te-form purpose in here

Question

でも傘に穴空いてて髪が濡れた　

I understand the message in this "But, my umbrella had a hole in it so my hair got wet"

But I don't quite get what it's the te-form in 穴空いてて is doing, is it the te form of compound sentence meaning "and" so the literal translation would be:

"But the umbrella had a hole in it and my hair got wet."

Also a friend of mine told me the quote could become:

でも傘に穴空いている、だから髪が濡れた。

So it confused me a bit because it made it seem that he is saying that, that te-form is the same as だから...

also, 穴空いている could be 穴が空いている?

Thanks.

Answer 1

でも傘に穴あいてて髪が濡れた。

＝「でも、傘に穴があいて（開いて）いて、髪が濡れた。」の口語の短縮表現。

・・・・・・・・・・

開いていて＝「開いている」の連用形「開いてい」に接続助詞「て」がついたもの。

開いている＝か行五段活用動詞「あく」の連用形「あい」に、接続助詞「て」がつき、補助動詞であり、上一段動詞である「いる」が付いたもの。

・・・・・・・・・・・・・・

かさに穴が開いていて is the cause and 髪が濡れた is the result. Therefore, the te-form functions as rather "because", "since," and "as" than "and."

"But the umbrella had a hole in it and my hair got wet."

This is not bad. However,

"But my hair got wet because the umbrella had a hole in it."

This is a better interpretation if this is a Japanese exam. Personally, however, I don't care much whether the conjunction, te-form, is "because" or "and" in this context. They do not change the meaning. They are more or less the same.