(), Marina HARALAMPIDOU Department of Mathematics, University of Athens
(), Marina HARALAMPIDOU Department of Mathematics, University of Athens

Section III.14. Factor Groups
Section III.14. Factor Groups

Cobordism of pairs
Cobordism of pairs

Quiz-2 Solutions
Quiz-2 Solutions

Draft version F ebruary 5, 2015
Draft version F ebruary 5, 2015

... operator on the collection P(X), the set of all subsets of X, which will become a closure operator. The closure operator gives a topology T ∗ on X (see [7]). This new topology is finer than the starting topology. In almost all of the earlier works on ideal topological spaces some subsets of the topo ...
STABLE HOMOTOPY THEORY 1. Spectra and the stable homotopy
STABLE HOMOTOPY THEORY 1. Spectra and the stable homotopy

6 | Continuous Functions
6 | Continuous Functions

§5 Manifolds as topological spaces
§5 Manifolds as topological spaces

Metrizability of hereditarily normal compact like groups1
Metrizability of hereditarily normal compact like groups1

Splitting of the Identity Component in Locally Compact Abelian Groups
Splitting of the Identity Component in Locally Compact Abelian Groups

Topology notes - University of Arizona
Topology notes - University of Arizona

Topics in uniform continuity
Topics in uniform continuity

Mat 247 - Definitions and results on group theory Definition: Let G be
Mat 247 - Definitions and results on group theory Definition: Let G be

RELATIONS BETWEEN UNION AND INTERSECTION OF IDEALS
RELATIONS BETWEEN UNION AND INTERSECTION OF IDEALS

Lecture 8
Lecture 8

topological closure of translation invariant preorders
topological closure of translation invariant preorders

§5 Manifolds as topological spaces
§5 Manifolds as topological spaces

Topological ordered spaces as a foundation for a quantum
Topological ordered spaces as a foundation for a quantum

... History of science suggests: let them be dynamical Some of these levels have become dynamical in the evolution of science: e.g. the rigid Euclidean space metric of classical mechanics has been replaced by the the dynamical Lorentzian metric of general relativity. We expect that the same process shou ...
Chapter 2 Metric Spaces and Topology
Chapter 2 Metric Spaces and Topology

On Locally compact groups whose set of compact subgroups is
On Locally compact groups whose set of compact subgroups is

§5 Manifolds as topological spaces
§5 Manifolds as topological spaces

Metric Spaces - Andrew Tulloch
Metric Spaces - Andrew Tulloch

One-point connectifications
One-point connectifications

Lecture 8
Lecture 8

Section 1.0.4.
Section 1.0.4.

Fundamental group

In the mathematics of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a topological invariant: homeomorphic topological spaces have the same fundamental group.Fundamental groups can be studied using the theory of covering spaces, since a fundamental group coincides with the group of deck transformations of the associated universal covering space. The abelianization of the fundamental group can be identified with the first homology group of the space. When the topological space is homeomorphic to a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations.Henri Poincaré defined the fundamental group in 1895 in his paper ""Analysis situs"". The concept emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Poincaré, and Felix Klein. It describes the monodromy properties of complex-valued functions, as well as providing a complete topological classification of closed surfaces.