Point Set Topology
Point Set Topology

Topology Proceedings - topo.auburn.edu
Topology Proceedings - topo.auburn.edu

Separation of Fuzzy Topological Space
Separation of Fuzzy Topological Space

The combinatorial structure of the Hawaiian earring group
The combinatorial structure of the Hawaiian earring group

Section 26. Compact Sets - Faculty
Section 26. Compact Sets - Faculty

On the open continuous images of paracompact Cech complete
On the open continuous images of paracompact Cech complete

A shorter proof of a theorem on hereditarily orderable spaces
A shorter proof of a theorem on hereditarily orderable spaces

Paracompact subspaces - Research Showcase @ CMU
Paracompact subspaces - Research Showcase @ CMU

Assignment 2 SOLUTION MATH 6540 (1) Show that a subset K of a
Assignment 2 SOLUTION MATH 6540 (1) Show that a subset K of a

Fixed Point in Minimal Spaces
Fixed Point in Minimal Spaces

generalized topological vector subspaces
generalized topological vector subspaces

Modern index theory CIRM
Modern index theory CIRM

On the topology of pointwise convergence on the boundaries of L_1
On the topology of pointwise convergence on the boundaries of L_1

Free full version - topo.auburn.edu
Free full version - topo.auburn.edu

Topology I with a categorical perspective
Topology I with a categorical perspective

The way-below relation of function spaces over semantic domains
The way-below relation of function spaces over semantic domains

E∞-Comodules and Topological Manifolds A Dissertation presented
E∞-Comodules and Topological Manifolds A Dissertation presented

... Chapter 2 contains, as Theorem 2.3.4, the second main technical result of this work. It states that the category of complexes of sheaves over an ordered simplicial complex X with values in Ab embeds, as a full differential graded subcategory, into the category of comodules over the S-coalgebra C• (X ...
S -compact and β S -closed spaces
S -compact and β S -closed spaces

... semi-open ,pre-open,  -open) set of X contained in A is called the S -interior (resp., semi-interior, pre-interior,  interior) of A and denoted by S  intA (resp., sintA , pintA ,  intA). The family of all S  -open (resp., semi-open, pre- ...
COUNTABLE DENSE HOMOGENEOUS BITOPOLOGICAL SPACES
COUNTABLE DENSE HOMOGENEOUS BITOPOLOGICAL SPACES

pdf
pdf

remarks on locally closed sets
remarks on locally closed sets

Introduction to basic topology and metric spaces
Introduction to basic topology and metric spaces

... Definition 2.6. A base for a topology τ is a subfamily β ⊂ τ such that every element of τ can be written as union of elements of β. A topological space with a countable base is called second countable. A base of neighborhoods of a point x ∈ X is a collection B of open neighborhoods of x such that an ...
DESCENT OF DELIGNE GROUPOIDS 1. Introduction 1.1. A formal
DESCENT OF DELIGNE GROUPOIDS 1. Introduction 1.1. A formal

PDF
PDF

An Introduction to Simplicial Sets
An Introduction to Simplicial Sets

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.