Can I drop the は in these two sentences?
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This is the contrastive は. This can be readily seen in the first sentence where emphasis is being placed on where in particular the individual is unable to study: neither at home nor in the library. This contrasts with other places where one might be able to study.
In the second sentence, attention is being drawn to Tokyo itself. Other places may not, by comparison, have so many people.
If in the first example, it had been written,
This sounds a bit mechanical. "I can't study at home. I can't study in the library." The listener might be thinking, "why are you telling me this?"
With は and も
this accomplished what we would accomplish in English by placing audible emphasis on "at home" and on "nor at the library" (nor corresponds with も). We expect these places to be good places to study; the use of は and も help clarify for the listener why they should care. If I wanted to convey this emphasis in written English, I could express this sentence as
I can neither study at home; nor can I study in the library.
This could have been expressed by
But は is drawing more attention to this exceptional fact.
omitting は would just sound like one's stating a fact about Tokyo giving absolutely no thought to how Tokyo compares to anywhere else. With は, Tokyo is being implicitly contrasted with other cities.
Without は, it's a bit like saying
Tokyo has a population of 37,194,105 people.
OK. Nice fact. You wouldn't think of the population of other cities because, well, every city has a population. The は, however, is saying, "Tokyo has a lot of folk [when compared to other cities]".
It’s because if you drop は, the sentences become topicless, which is not necessarily valid. In other words, a sentence without は is not neutral.