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R. Engelking: General Topology Introduction 1 Topological spaces
R. Engelking: General Topology Introduction 1 Topological spaces

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

Characterizing continuous functions on compact
Characterizing continuous functions on compact

... Aside from introduced notions, our notation and terminology are standard, as found in the book by Engelking [2]. In particular an ordinal is the set of its predecessors so that for example 2 = {0, 1}. The cardinality of the continuum is denoted by c and we use ω to denote both ℵ0 and the set of natu ...
Ultrafilters and Independent Systems - KTIML
Ultrafilters and Independent Systems - KTIML

Covariance algebra of a partial dynamical system - MATH Mail
Covariance algebra of a partial dynamical system - MATH Mail

... 2) we obtain a rather thorough description of the associated covariance algebra, and also strong tools to study it, 3) we find points of contact of different approaches and thereby clarify the relations between them. In order to give the motivation of the construction of the crossed product develope ...
Full paper - New Zealand Journal of Mathematics
Full paper - New Zealand Journal of Mathematics

A primer on homotopy colimits
A primer on homotopy colimits

5 Solution of Homework
5 Solution of Homework

Basic Concepts of Point Set Topology
Basic Concepts of Point Set Topology

ABSOLUTELY CLOSED SPACES
ABSOLUTELY CLOSED SPACES

Some Properties of Almost Contra-Precontinuous Functions
Some Properties of Almost Contra-Precontinuous Functions

hohology of cell complexes george e. cooke and ross l. finney
hohology of cell complexes george e. cooke and ross l. finney

... of a finite number of (open) cells-- and b) weak topology-­ the topology on the underlying topological space is the weak topology with respect to the closed cells of the complex.) We g i ve se veral examples of complexes, regular and irregular, and comple te the chapter with a section on simplici al ...
to PDF file
to PDF file

Topological Cones: Functional Analysis in a T0
Topological Cones: Functional Analysis in a T0

Convex Optimization in Infinite Dimensional Spaces*
Convex Optimization in Infinite Dimensional Spaces*

A BRIEF INTRODUCTION TO SHEAVES References 1. Presheaves
A BRIEF INTRODUCTION TO SHEAVES References 1. Presheaves

Chapter 5 Manifolds, Tangent Spaces, Cotangent Spaces
Chapter 5 Manifolds, Tangent Spaces, Cotangent Spaces

NON-ARCHIMEDEAN ANALYTIFICATION OF ALGEBRAIC
NON-ARCHIMEDEAN ANALYTIFICATION OF ALGEBRAIC

... of analytic extension similarly (allowing trivial absolute values). By abuse of notation, if x is a point in a k-analytic space X then we write (X, x) to denote the associated germ (denoted Xx in [T1], [T2]). We require algebraic spaces to have quasi-compact diagonal over Spec Z, and an étale chart ...
Partial Metric Spaces - Department of Computer Science
Partial Metric Spaces - Department of Computer Science

1. Introduction 1 2. Simplicial and Singular Intersection Homology 2
1. Introduction 1 2. Simplicial and Singular Intersection Homology 2

Topological and Nonstandard Extensions
Topological and Nonstandard Extensions

Introduction to Topology
Introduction to Topology

General Topology - Institut for Matematiske Fag
General Topology - Institut for Matematiske Fag

GENERIC SUBGROUPS OF LIE GROUPS 1. introduction In this
GENERIC SUBGROUPS OF LIE GROUPS 1. introduction In this

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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.
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