Besides the fact that it's exciting and well written, its portrayal of slavery is especially significant. At first blush you might think that Stowe whitewashes slavery, since we see not one but two examples of slavers who are basically good people and treat their slaves like family. But the protagonist, Uncle Tom, is not permitted to keep either master for long. The first very reluctantly sells him in order to pay off debts, and the second is suddenly killed on the way to signing his free papers, leaving Tom's fate in the hands of the second master's much less sympathetic wife. Tom is sold again and finally ends up with the worst imaginable master, a great muscular villain whose personal mission seems to be to make his slaves suffer. The moral is that the real problem with American slavery of blacks was not the particular temperaments or habits of the slavers or the particular society in which slavery flourished but slavery itself—the whole notion of people being property. So long as people are property, they can never be truly safe or free, because however moral their current masters are, they're one accident away from another chance of being treated like dogs. Indeed, Stowe repeatedly stresses the conflict between the personhood and objectification of slaves, as in a scene where a slave commits suicide and her master coolly writes her off as a loss in his ledger.
Stowe's portrayal of Tom himself also deserves more credit than it gets. "Uncle Tom" has become a byword for meek submission, but Tom is anything but meek. He scrupulously takes no opportunities to escape not out of fear or internalized racism but out of sheer respect for the law of man. He does any work he's ordered to do, regardless of danger to himself—but he draws the line at harming others, taking enormous abuse at the hands of overseers when he defies their attempts to turn him into an abusive overseer. Even when his fellow slaves tell him to submit to the overseers for his own good, and his master makes clear he'll readily kill him as an example to the others, Tom never wavers, sustained by raw religious conviction alone. Now that's a Christianity I can believe in. And in case you thought Stowe believed that the only good slave was a lawful-good slave, she provides a chaotic-good counterpart. George, a slave who's smarter than his master, hears that he's to be separated from his family and, enraged, escapes with them to Canada, where they all live happily ever after.
tl;dr: I think Uncle Tom's Cabin is a pretty cool guy. eh resists eivl and doesnt afraid of anything.
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If f_n is continuous on [a, b] for all n, (f_n(x)) is nonincreasing for each x, and (f_n) goes pointwise to a continuous f, then (f_n) goes to f uniformly.