THEORY OF COVERING SPACES
THEORY OF COVERING SPACES

NOTE ON COFIBRATION In this overview I assume
NOTE ON COFIBRATION In this overview I assume

Lowen LM-fuzzy topological spaces
Lowen LM-fuzzy topological spaces

On Colimits in Various Categories of Manifolds
On Colimits in Various Categories of Manifolds

Various Notions of Compactness
Various Notions of Compactness

A NEW TOPOLOGY FROM AN OLD ONE Halgwrd Mohammed
A NEW TOPOLOGY FROM AN OLD ONE Halgwrd Mohammed

Introduction to weakly b- transitive maps on topological spaces
Introduction to weakly b- transitive maps on topological spaces

PDF
PDF

Groups acting on sets
Groups acting on sets

SECTION 2: UNIVERSAL COEFFICIENT THEOREM IN SINGULAR
SECTION 2: UNIVERSAL COEFFICIENT THEOREM IN SINGULAR

Ideal Resolvability - Mathematics TU Graz
Ideal Resolvability - Mathematics TU Graz

Metric and Banach spaces
Metric and Banach spaces

... Theorem B.2 Let (X, dX ) and (Y, dY ) be two metric spaces and let consider a uniformely continuous function f : (X, dX ) → (Y, dY ). If (xn )n∈N is a Cauchy sequence of X, then f (xn )n∈N is a Cauchy sequence of F . The reciprocal one is not true. Proposition B.6 We have two properties about conver ...
Banach spaces
Banach spaces

ON SEQUENTIAL PROPERTIES OF NOETHERIAN TOPOLOGICAL
ON SEQUENTIAL PROPERTIES OF NOETHERIAN TOPOLOGICAL

T-Spaces - Tubitak Journals
T-Spaces - Tubitak Journals

4. Compactness
4. Compactness

The Lattice of Domains of an Extremally Disconnected Space 1
The Lattice of Domains of an Extremally Disconnected Space 1

Local isometries on spaces of continuous functions
Local isometries on spaces of continuous functions

PDF
PDF

... well-ordered set. W (α) becomes a topological space if we equip W (α) with the interval topology. An ordinal space X is a topological space such that X = W (α) (with the interval topology) for some ordinal α. In this entry, we will always assume that W (α) 6= ∅, or 0 < α. Before examining some basic ...
An Introduction to Topological Groups
An Introduction to Topological Groups

Finite-to-one open maps of generalized metric spaces
Finite-to-one open maps of generalized metric spaces

Chapter 9 The Topology of Metric Spaces
Chapter 9 The Topology of Metric Spaces

THEOREMS ON COMPACT TOTALLY DISCONNECTED
THEOREMS ON COMPACT TOTALLY DISCONNECTED

SOME CLASSICAL SPACES REALIZED AS MUTATIONAL SPACES
SOME CLASSICAL SPACES REALIZED AS MUTATIONAL SPACES

THE CONVERSE OF THE INTERMEDIATE VALUE THEOREM
THE CONVERSE OF THE INTERMEDIATE VALUE THEOREM

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.