Artículos con la etiqueta ‘General Topology (math.GN)’

Set theory and topology. An introduction to the foundations of analysis. Part II: Topology – Fundamental notions

Por • 4 jul, 2013 • Category: Opinion

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as well as their applications to real numbers. Various methods to construct topological spaces are presented.

The Shape of Infinity

Por • 21 sep, 2012 • Category: Opinion

In these expository notes, intended for students without background in point-set topology, we develop the basic theory of the Stone-Cech compactification without reference to open sets, closed sets, filters, or nets. In particular, this means we cannot use any of the usual definitions of topological space. This may seem like proposing to run a marathon while hopping on one foot, but it is easier than it may appear, and not devoid of interest. We use gauge spaces (uniform spaces presented by a family of pseudometrics); we define compactness as total boundedness plus completeness; and we define completeness using a variation on Lawvere’s categorical characterization of completeness for metric spaces.