THE EULER CLASS OF A SUBSET COMPLEX 1. Introduction Let G
THE EULER CLASS OF A SUBSET COMPLEX 1. Introduction Let G

A study on compactness in metric spaces and topological spaces
A study on compactness in metric spaces and topological spaces

Lecture notes up to 08 Mar 2017
Lecture notes up to 08 Mar 2017

Recent Progress in the Theory of Generalized Closed Sets ∗
Recent Progress in the Theory of Generalized Closed Sets ∗

... the sense of N. Levine, and their relationships to other classes of sets such as α-open sets, semi-open sets and preopen sets. This investigation has led to significant contributions to the theories of separation axioms, covering properties and generalizations of continuity. In this paper we shall g ...
Complex cobordism of Hilbert manifolds with some applications to
Complex cobordism of Hilbert manifolds with some applications to

THEORY OF FREDHOLM OPERATORS AND
THEORY OF FREDHOLM OPERATORS AND

6. Metric spaces
6. Metric spaces

Aspherical manifolds that cannot be triangulated
Aspherical manifolds that cannot be triangulated

4. Topologies and Continuous Maps.
4. Topologies and Continuous Maps.

TOPOLOGICAL EQUIVALENCES FOR DIFFERENTIAL GRADED
TOPOLOGICAL EQUIVALENCES FOR DIFFERENTIAL GRADED

Group cohomology - of Alexey Beshenov
Group cohomology - of Alexey Beshenov

Generalized Minimal Closed Sets in Topological Spaces.
Generalized Minimal Closed Sets in Topological Spaces.

NOTES FOR MATH 4510, FALL 2010 1. Metric Spaces The
NOTES FOR MATH 4510, FALL 2010 1. Metric Spaces The

On Some Paracompactness%type Properties of Fuzzy Topological
On Some Paracompactness%type Properties of Fuzzy Topological

one-point compactification on convergence spaces
one-point compactification on convergence spaces

9. Sheaf Cohomology Definition 9.1. Let X be a topological space
9. Sheaf Cohomology Definition 9.1. Let X be a topological space

Homotopy Theory of Topological Spaces and Simplicial Sets
Homotopy Theory of Topological Spaces and Simplicial Sets

Chapter 1: Basic point set topology
Chapter 1: Basic point set topology

QUOTIENTS OF PROXIMITY SPACES 589
QUOTIENTS OF PROXIMITY SPACES 589

Several approaches to non-archimedean geometry
Several approaches to non-archimedean geometry

... can be proved for convergent power series over k by adapting the traditional proofs over R and C. Serre’s Harvard lectures [S] on Lie groups and Lie algebras develop this point of view, for example. However, these kinds of spaces have limited geometric interest because they are totally disconnected. ...
Elementary Topology Problem Textbook O. Ya. Viro, OA
Elementary Topology Problem Textbook O. Ya. Viro, OA

Reachability and Connectivity Queries in Constraint Databases
Reachability and Connectivity Queries in Constraint Databases

derived smooth manifolds
derived smooth manifolds

Generalized Dihedral Groups - College of Arts and Sciences
Generalized Dihedral Groups - College of Arts and Sciences

S. Jothimani, T. Jenitha Premalatha Πgβ Normal Space in Intuitioitic
S. Jothimani, T. Jenitha Premalatha Πgβ Normal Space in Intuitioitic

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.