generated from smyalygames/quartz
788 B
788 B
Definition
We say f is continuous (at every x) if f^{-1}(A) \equiv \{ x \in X | f(x) \in A \} is open for every open A \subset Y.
We say f is Open Sets if f(B) is Open Sets and \forall Open Sets B \subset X.
If f is a Bijective that is both continuous and Open Sets, it is a Homeomorphic, and X and Y are Homeomorphic, written X \simeq Y; they are the 'same' as Topological Space.
In-depth Definition
A function f : X \to Y between Topological Space is continuous at $x \in X$ if for every neighbourhood A of f(x), we can find a neighbourhood B of x such that f(B) \subset A, or B \subset f^{-1}(A).