Introduction to topological spaces # We want now to extend the idea of continuity presented in limits , which is a function f : E n → E n is continuous if given x then ∀ ε > 0 ∃ δ such that ∀ y : ∥ y − x ∥ < δ ⟹ ∥ f ( y ) − f ( x )∥ < ε . But we want to get rid of the…
There is a close relationship between topologies and metric spaces. We will see that every metric space directly induces a topology based on its metric. (from a CS point of view, this means topologies are more general than metric spaces). Definition of Metric Space # We say that…
This small note is an introduction to Topology that follows the introductory arguments of (Armstrong 2013) . Euler's Theorem # We will start our journey in topology following a classical example in the history of Mathematics the relation: v − e + f = 2 Valid for classical…