On Chains in H-Closed Topological Pospaces
On Chains in H-Closed Topological Pospaces

arXiv:0903.2024v3 [math.AG] 9 Jul 2009
arXiv:0903.2024v3 [math.AG] 9 Jul 2009

DIFFERENTIABLE GROUP ACTIONS ON HOMOTOPY SPHERES. II
DIFFERENTIABLE GROUP ACTIONS ON HOMOTOPY SPHERES. II

Topological rings. - ScholarWorks @ UMT
Topological rings. - ScholarWorks @ UMT

www.math.uwo.ca
www.math.uwo.ca

ON c-PRECONTINUOUS FUNCTIONS
ON c-PRECONTINUOUS FUNCTIONS

The Weil-étale topology for number rings
The Weil-étale topology for number rings

6. Compactness
6. Compactness

Lecture 1: August 25 Introduction. Topology grew out of certain
Lecture 1: August 25 Introduction. Topology grew out of certain

class notes - Math User Home Pages
class notes - Math User Home Pages

On slight homogeneous and countable dense homogeneous spaces
On slight homogeneous and countable dense homogeneous spaces

... Theorem 2.2 they are slightly homogeneous. The disjoint sum of ((0, 1), τu ) and ({3}, τu ) is not slightly homogeneous because there is no slight homeomorphism f : ((0, 1) ∪ {3}), τu ) → ((0, 1) ∪ {3}), τu ) such that f (3) = 12 . Theorem 2.16. Let (X, τ ) be a space which contains a non-empty clop ...
Simplicial sets
Simplicial sets

... difficulty is that the cartesian product of two simplices of positive dimension is not a simplex. As a consequence, there is no natural operation of a cartesian product on simplicial complexes. Finally, there is no notion of a quotient simplicial complex, which would be necessary for many constructi ...
On slightly I-continuous Multifunctions 1 Introduction
On slightly I-continuous Multifunctions 1 Introduction

Real analysis
Real analysis

minimal convergence spaces - American Mathematical Society
minimal convergence spaces - American Mathematical Society

II. General theory of locally compact groups
II. General theory of locally compact groups

ON THE TOPOLOGY OF WEAKLY AND STRONGLY SEPARATED
ON THE TOPOLOGY OF WEAKLY AND STRONGLY SEPARATED

H48045155
H48045155

A NOTE ON COMPACT SEMIRINGS
A NOTE ON COMPACT SEMIRINGS

Smooth manifolds - University of Arizona Math
Smooth manifolds - University of Arizona Math

... : R ! R is de…ned by (x) = x1=3 : This is an atlas. Note, however, that with this atlas, f : R ! R given by f (x) = x1=3 is a smooth function, since ...
City Research Online
City Research Online

MA651 Topology. Lecture 11. Metric Spaces 2.
MA651 Topology. Lecture 11. Metric Spaces 2.

NU2422512255
NU2422512255

Topological classification of surfaces
Topological classification of surfaces

On Relative Preclosedness of Strongly Compact (Countably p
On Relative Preclosedness of Strongly Compact (Countably p

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.