2 ms·
The requirement for finiteness means you are just working with lattices. Topology approached via frame homomorphisms (like in the nlab book) makes this clear.
by openfuture 6y ago
The requirement for finiteness means you are just working with lattices. Topology approached via frame homomorphisms (like in the nlab book) makes this clear.
Disclaimer: not a mathematician (yet)
- taliesinb 6y agoThanks! 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?
- openfuture 6y agoI 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 https://ncatlab.org/nlab/show/Introduction+to+Topology [2]: https://ncatlab.org/nlab/show/frame https://ncatlab.org/nlab/show/frame