Modal compact Hausdorff spaces
Modal compact Hausdorff spaces

TOTALLY α * CONTINUOUS FUNCTIONS IN TOPOLOGICAL SPACES
TOTALLY α * CONTINUOUS FUNCTIONS IN TOPOLOGICAL SPACES

Non-archimedean analytic spaces
Non-archimedean analytic spaces

... points with trivial kernels. To give the latter is the same as to extend the valuation on k to k (T ). For example, to each disc with center at aP of radius r we associate its maximal point pa,r given by | ai (T − a)i | = max |ai |r i . X is a (sort of) infinite tree and classical points are its lea ...
ON A WEAK FORM OF WEAK QUASI
ON A WEAK FORM OF WEAK QUASI

new characterization of kernel set in fuzzy topological spaces
new characterization of kernel set in fuzzy topological spaces

Some results on sequentially compact extensions
Some results on sequentially compact extensions

Geometric structures on 3–manifolds - bcf.usc.edu
Geometric structures on 3–manifolds - bcf.usc.edu

GOOD MEASURES ON CANTOR SPACE Introduction A Cantor
GOOD MEASURES ON CANTOR SPACE Introduction A Cantor

... that it is conjugate to the product of the identity on X with the translation map of the universal adding machine. 1. The clopen values invariants All of our topological spaces will be nonempty Polish spaces. That is, they are separable and completely metrizable. Furthermore, unless we mention other ...
ON THE OPPOSITE OF THE CATEGORY OF RINGS
ON THE OPPOSITE OF THE CATEGORY OF RINGS

MAPPING CYLINDERS AND THE OKA PRINCIPLE Finnur Lárusson
MAPPING CYLINDERS AND THE OKA PRINCIPLE Finnur Lárusson

Weyl Groups Associated with Affine Reflection Systems of Type
Weyl Groups Associated with Affine Reflection Systems of Type

Regular Weakly Continuous Functions in Ideal Topological Spaces
Regular Weakly Continuous Functions in Ideal Topological Spaces

Generalized rough topological spaces
Generalized rough topological spaces

ON EXPONENTIABLE SOFT TOPOLOGICAL SPACES 1
ON EXPONENTIABLE SOFT TOPOLOGICAL SPACES 1

T A G Coarse homology theories
T A G Coarse homology theories

METRIC AND TOPOLOGICAL SPACES
METRIC AND TOPOLOGICAL SPACES

INVARIANCE OF FUZZY PROPERTIES Francisco Gallego Lupiañez
INVARIANCE OF FUZZY PROPERTIES Francisco Gallego Lupiañez

Measures on minimally generated Boolean algebras
Measures on minimally generated Boolean algebras

Groupoid C*-algebras with Hausdorff Spectrum
Groupoid C*-algebras with Hausdorff Spectrum

ON STRONGLY θ-e-CONTINUOUS FUNCTIONS 1. Introduction The
ON STRONGLY θ-e-CONTINUOUS FUNCTIONS 1. Introduction The

Metric geometry of locally compact groups
Metric geometry of locally compact groups

An Introduction to Unitary Representations of Lie Groups
An Introduction to Unitary Representations of Lie Groups

The Urysohn Metrization Theorem
The Urysohn Metrization Theorem

A note on reordering ordered topological spaces and the existence
A note on reordering ordered topological spaces and the existence

A Topological Study of Tilings
A Topological Study of Tilings

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.