MANIFOLDS, COHOMOLOGY, AND SHEAVES
MANIFOLDS, COHOMOLOGY, AND SHEAVES

Section 18. Continuous Functions - Faculty
Section 18. Continuous Functions - Faculty

Continuity in Fine-Topological Space
Continuity in Fine-Topological Space

of almost compact spaces - American Mathematical Society
of almost compact spaces - American Mathematical Society

Support Sets of Distributions with Given Interaction Structure
Support Sets of Distributions with Given Interaction Structure

Equivariant cohomology and equivariant intersection theory
Equivariant cohomology and equivariant intersection theory

Lectures on Order and Topology
Lectures on Order and Topology

FINITE TOPOLOGIES AND DIGRAPHS
FINITE TOPOLOGIES AND DIGRAPHS

Open subgroups and Pontryagin duality
Open subgroups and Pontryagin duality

Reduced coproducts of compact Hausdorff spaces
Reduced coproducts of compact Hausdorff spaces

To be published in Comment. Math. Univ. Carolinae CONTINUOUS
To be published in Comment. Math. Univ. Carolinae CONTINUOUS

The cartesian closed topological hull of the category of completely
The cartesian closed topological hull of the category of completely

Homomorphisms - EnriqueAreyan.com
Homomorphisms - EnriqueAreyan.com

ON METRIZABLE ENVELOPING SEMIGROUPS 1. Introduction A
ON METRIZABLE ENVELOPING SEMIGROUPS 1. Introduction A

Lectures on Order and Topology
Lectures on Order and Topology

bornological countable enlargements
bornological countable enlargements

D-COMPLETIONS AND THE d-TOPOLOGY 1. Introduction In the
D-COMPLETIONS AND THE d-TOPOLOGY 1. Introduction In the

Selection principles and infinite games on multicovered spaces
Selection principles and infinite games on multicovered spaces

Topological Groups Part III, Spring 2008
Topological Groups Part III, Spring 2008

... group for each α ∈ A. Their complete direct product is G = α Gα equipped with the usual product topology τG and with multiplication given by (x ×G y)α = xα ×α yα . Definition 4.2. Suppose A is non-empty and (Gα , ×α ) is a group Q for each α ∈ A. Their direct product is the subgroup of the group G = ...
SOME RESULTS ON C(X) WITH SET OPEN TOPOLOGY
SOME RESULTS ON C(X) WITH SET OPEN TOPOLOGY

Continuous cohomology of groups and classifying spaces
Continuous cohomology of groups and classifying spaces

... If G and K are not connected, one has to introduce the slight modification denoted H(g9 K; A) defined by replacing (2) above by (2') w is invariant under the action of K. If G is not compact we need to assume there is at least some "compact form" Gu, that is a compact connected Lie group having the ...
RgI-closed Sets in Ideal Topological Spaces
RgI-closed Sets in Ideal Topological Spaces

Ig−Submaximal Spaces Key Words:Ideal topological space
Ig−Submaximal Spaces Key Words:Ideal topological space

POSET FIBER THEOREMS 1. Introduction In an influential paper
POSET FIBER THEOREMS 1. Introduction In an influential paper

Midterm for MATH 5345H: Introduction to Topology October 14, 2013
Midterm for MATH 5345H: Introduction to Topology October 14, 2013

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.