A topology T for a space X gives a rough notion of proximity (eventually relevant for sequences and analysis) and also induces a system of directed arrows on the power set. Continuous functions are an easily definable class of maps special for that topology from or to X and those in turn often translate to morphisms of object on that space. The definitions is actually so rudimentary that it gives rise to dualities all over the place (see Stone duality, Gelfand representation theorems, models for non-classical logics, and stronger notions of topologies (Grothendieck topoi) merge with an even broader class of relevant mathematical objects) It's also a tool to classify sets with other structure (or let's say spaces).
All trademarks and copyrights on this page are owned by their respective parties. Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
This is a 4chan archive - all of the shown content originated from that site. This means that 4Archive shows their content, archived. If you need information for a Poster - contact them.
If a post contains personal/copyrighted/illegal content, then use the post's [Report] link! If a post is not removed within 24h contact me at email@example.com with the post's information.