A CONVENIENT CATEGORY FOR DIRECTED HOMOTOPY
A CONVENIENT CATEGORY FOR DIRECTED HOMOTOPY

New Separation Axioms Using the idea of "Gem
New Separation Axioms Using the idea of "Gem

METRIZABILITY OF RECTIFIABLE SPACES 1. Introduction Recall
METRIZABILITY OF RECTIFIABLE SPACES 1. Introduction Recall

On Preclosed Sets and Their Generalizations
On Preclosed Sets and Their Generalizations

ON THE COVERING TYPE OF A SPACE From the point - IMJ-PRG
ON THE COVERING TYPE OF A SPACE From the point - IMJ-PRG

THE INTERSECTION OF TOPOLOGICAL AND METRIC SPACES
THE INTERSECTION OF TOPOLOGICAL AND METRIC SPACES

Problem Farm
Problem Farm

A S - Alex Suciu
A S - Alex Suciu

... variety which deform-retracts onto the singularity link, M. The almost free C˚ -action on X ˚ restricts to an S 1 -action on M with finite isotropy subgroups. In particular, M is an orientable Seifert fibered 3-manifold. The orbit space, M{S 1 “ X ˚ {C˚ , is a smooth projective curve Σg , of genus g ...
What is a Bohr compactification
What is a Bohr compactification

Cones on homotopy probability spaces
Cones on homotopy probability spaces

Toposym Kanpur - DML-CZ
Toposym Kanpur - DML-CZ

... Theorem 2. Let M be a dense generalized closed jS-CP subset of a normal space (X, SГ). Then (X, SГ) is CP. Proof. We first prove that M is a normal subspace. The intersection of a closed and a generalized closed subset is a generalized closed subset. So if H is closed in M, then H is a generalized c ...
Projective limits of topological vector spaces
Projective limits of topological vector spaces

Topology Proceedings H-CLOSED SPACES AND H
Topology Proceedings H-CLOSED SPACES AND H

Let X,d be a metric space.
Let X,d be a metric space.

... 38) A (nonempty) subset of R is connected iff it is an interval. 39) As with compactness, a subset C of a metric space X is connected as a subset of X iff it is connected as a subset of itself (with the metric it inherits from X). 40) Continuous images of connected sets are connected. 41) Let f : A ...
Section 41. Paracompactness - Faculty
Section 41. Paracompactness - Faculty

TOPOLOGICAL GROUPS AND CONVEX SETS HOMEOMORPHIC
TOPOLOGICAL GROUPS AND CONVEX SETS HOMEOMORPHIC

GALOIS DESCENT 1. Introduction
GALOIS DESCENT 1. Introduction

GALOIS DESCENT 1. Introduction Let L/K be a field extension. A K
GALOIS DESCENT 1. Introduction Let L/K be a field extension. A K

... is the “right” definition of a K-form,1 although the other properties are arguably a better way to understand what the concept is all about (or even to recognize it in concrete cases like Examples 1.2, 1.3, and 1.4.) In the C/R-case, R-forms of a complex vector space are parametrized by the conjugat ...
Higher algebra and topological quantum field theory
Higher algebra and topological quantum field theory

a note on trivial fibrations - Fakulteta za matematiko in fiziko
a note on trivial fibrations - Fakulteta za matematiko in fiziko

... A fibration F ,→ E −→ B is fibre-homotopy trivial if it is fibre-homotopy equivalent to the product fibration prB : B × F → B. A fibration is locally trivial if there is a covering {Uλ } of the base B, suche that the restrictions p : p−1 (Uλ ) → Uλ are fibre-homotopy trivial. We usually require that ...
Cantor`s Theorem and Locally Compact Spaces
Cantor`s Theorem and Locally Compact Spaces

Solenoids
Solenoids

PDF
PDF

Math 535 - General Topology Fall 2012 Homework 8 Solutions
Math 535 - General Topology Fall 2012 Homework 8 Solutions

The Hausdorff Quotient
The Hausdorff Quotient

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.