Basic Topology
In mathematics, topology (from the Greek words τόπος, 'place', and λόγος, 'study') is
concerned with the properties of a geometric
object that are
preserved under continuous deformations, such as stretching, twisting, crumpling and
bending, but not tearing or gluing.
To understand what a
topological space is, there are a number of definitions and issues that we need
to address first. Namely, we will discuss metric spaces, open sets, and closed
sets. Once we have an idea of these terms, we will have the vocabulary to define
a topology. The definition of topology will also give us a more generalized
notion of the meaning of open and closed sets.