In a conversation between a student (Mike) and his teacher:
先生: ええ。[子供の]頃、私の家の近くに柔道をやっていてとても元気な子供がいてね。
the latter ends the sentence with the ~て form. Why is that so? I would expect the sentence to end with いました rather than いて, since he is speaking about a past time and he is ending all the other sentences with the polite marker です.
I found a related question with its answer about another sentence ending in ~て in a different context. In that case, the ~て ending is used to "imply that the speaker has something more to say". I'm not sure if it's also the case in the sentence we are discussing here, because the conversation continues after that. If this is another case of a sentence where it's implied that there's more to say, what would that extra information be? And if it's not the case, what else is going on here?
For your reference, this is the full conversation:
よろしくお願いします