Question
Asked 18th Jun, 2014
Demetris Christopoulos
- National and Kapodistrian University of Athens
What is the essential difference between Algebra and Topology?
[A] Let X\neq\emptyset and \tau\in P[x], where P[X] is the power set of X. Then if we have that:
i] X,\emptyset\in\tau
ii] i\in I, A_{i}\in\tau \Rightarrow \cup_{i\in I}{A_{i}} \in \Tau
iii] j\in J, J finite, A_{j}\in \tau \Rightarrow \cap_{j\in J}{A_{j}}\in \tau
We say that the collection \tau is a Topology in X and that [X,\tau] is a topological space.
[B] The minimum requirement for every algebraic structure is closure under the defined binary operation.
What is the essential difference between Algebra & Topology?
Both of them are guided by the concept of closure.
So, why have we defined two branches that are almost of the same philosophy?
- 55.24 KBalgtop.pdf