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Thanks! By nlab book you mean the whole nlab project? Also, can you help me understand the connection to lattices? Do they model intersection and union of open sets? Why is finiteness needed for lattices to be appropriate?

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I meant [1] they use frames [2] to explain what a topology is but in a finite setting the frame becomes a lattice because you only have finite meets and joins.

[1]: https://ncatlab.org/nlab/show/Introduction+to+Topology [2]: https://ncatlab.org/nlab/show/frame

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