“ことはある” is often explained as the topical form of “ことがある” which simply means that things sometimes happen, or one has past experience with something when following a past verb.
However I keep seeing the “ことはある” and “ことはない” pattern as well seemingly as a way to topicalize the entire sentence in either a negative or positive way and nothing more. For instance one can say “まあ、ゲームは好きだけど、毎日する時間がない。” to say “Well, I do like video games, but I don't have the time to play them every day.” topicalizing “ゲーム” specifically, but I also see “ことはある” sometimes in a way that suggests that “ゲームが好きなことはあるけど、毎日する時間がない” is possible as well, seemingly not so much expressing that one “sometimes” likes videogames but topicalizing the entire “ゲームが好きだ” sentence rather than only the “ゲーム” part. Or for instance something like “仕事で忙しいことはないから、手伝ってあげるよ” which again would not express “never being busy with work” but used in a context where for some reason the listener might assume the speaker would be busy with work, with the speaker explicitly refuting that assumption.
Is this understanding correct or can “ことはある” only be used to express that something sometimes happens? Not affirm an assumption of something currently happening?
