Compact-like properties in hyperspaces
Compact-like properties in hyperspaces

Introduction to General Topology
Introduction to General Topology

A Topology Primer
A Topology Primer

On Almost Locally Compact Spaces
On Almost Locally Compact Spaces

... So X × Y is ALC. Lemma 2.8 . Let X ,Y be topological spaces and f : X → Y is an open onto almost continuous map. If X is nearly-compact then so is Y . Proof . Let X ,Y be topological spaces and f : X → Y is an open onto almost continuous map. Suppose X is nearly-compact and {Vα } is an open cover of ...
THE COHOMOLOGY RING OF FREE LOOP SPACES 1. Introduction
THE COHOMOLOGY RING OF FREE LOOP SPACES 1. Introduction

Countable dense homogeneous filters and the Menger covering
Countable dense homogeneous filters and the Menger covering

hw1.pdf
hw1.pdf

Introduction to Topology
Introduction to Topology

Measures - UC Davis Mathematics
Measures - UC Davis Mathematics

ON A CLASS OF SETS VIA GRILL : A DECOMPOSITION OF
ON A CLASS OF SETS VIA GRILL : A DECOMPOSITION OF

FURTHER DECOMPOSITIONS OF ∗-CONTINUITYI 1 Introduction
FURTHER DECOMPOSITIONS OF ∗-CONTINUITYI 1 Introduction

g*s-Closed Sets in Topological Spaces
g*s-Closed Sets in Topological Spaces

... 4. g*s –continuous functions in Topological spaces Levine [ 5 ] introduced semi continuous functions using semi open sets. The study on the properties of semi-continuous functions is further carried out by Noiri[ 8 ], crossely and Hildebrand and many others. Sundram [ 13 ] introduced the concept of ...
β1 -paracompact spaces
β1 -paracompact spaces

On the characterization of compact Hausdorff X for which C(X) is
On the characterization of compact Hausdorff X for which C(X) is

6. “× º - 筑波学院大学
6. “× º - 筑波学院大学

On productively Lindelöf spaces Michael Barr ∗ Department of
On productively Lindelöf spaces Michael Barr ∗ Department of

Compactness
Compactness

$\ alpha r $-spaces and some of their properties
$\ alpha r $-spaces and some of their properties

Between Preopen and Open Sets in Topological Spaces
Between Preopen and Open Sets in Topological Spaces

Embeddings from the point of view of immersion theory : Part I
Embeddings from the point of view of immersion theory : Part I

MINIMAL TOPOLOGICAL SPACES(`)
MINIMAL TOPOLOGICAL SPACES(`)

Manifolds and Topology MAT3024 2011/2012 Prof. H. Bruin
Manifolds and Topology MAT3024 2011/2012 Prof. H. Bruin

The subspace topology, ctd. Closed sets and limit points.
The subspace topology, ctd. Closed sets and limit points.

TOPOLOGICAL GROUPS 1. Introduction Topological groups are
TOPOLOGICAL GROUPS 1. Introduction Topological groups are

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

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.