Extending Baire–one functions on topological spaces ⋆
Extending Baire–one functions on topological spaces ⋆

18 Divisible groups
18 Divisible groups

Almost disjoint families and topology
Almost disjoint families and topology

S1-paracompactness with respect to an ideal
S1-paracompactness with respect to an ideal

Logical consequence and closure spaces
Logical consequence and closure spaces

... a closure operator on S characterized by extensivity (C1), idempotence (C2), and isotonicity (C3): ...
Stationary probability measures and topological realizations
Stationary probability measures and topological realizations

Algebraic Topology
Algebraic Topology

Introduction to Quad topological spaces(4-tuple topology)
Introduction to Quad topological spaces(4-tuple topology)

Localization of Ringed Spaces - Scientific Research Publishing
Localization of Ringed Spaces - Scientific Research Publishing

Groupoids in categories with pretopology
Groupoids in categories with pretopology

Topological Dynamics: Minimality, Entropy and Chaos.
Topological Dynamics: Minimality, Entropy and Chaos.

ROLLING OF COXETER POLYHEDRA ALONG MIRRORS 1
ROLLING OF COXETER POLYHEDRA ALONG MIRRORS 1

Notes from the Prague Set Theory seminar
Notes from the Prague Set Theory seminar

Some structure theorems for algebraic groups
Some structure theorems for algebraic groups

Localization of ringed spaces
Localization of ringed spaces

... Let Top, LRS, RS, and Sch denote the categories of topological spaces, locally ringed spaces, ringed spaces, and schemes, respectively. Consider maps of schemes fi : Xi → Y (i = 1, 2) and their fibered product X1 ×Y X2 as schemes. Let X denote the topological space underlying a scheme X. There is a ...
Embeddings of compact convex sets and locally compact cones
Embeddings of compact convex sets and locally compact cones

Relative Stanley–Reisner theory and Upper Bound Theorems for
Relative Stanley–Reisner theory and Upper Bound Theorems for

ON LI–YORKE PAIRS François Blanchard, Eli Glasner, Sergiı
ON LI–YORKE PAIRS François Blanchard, Eli Glasner, Sergiı

stationary probability measures and topological
stationary probability measures and topological

The Coarse Geometry of Groups
The Coarse Geometry of Groups

CROSSED PRODUCT STRUCTURES ASSOCIATED WITH
CROSSED PRODUCT STRUCTURES ASSOCIATED WITH

TOPOLOGY 004C Contents 1. Introduction 1 2. Basic notions 2 3
TOPOLOGY 004C Contents 1. Introduction 1 2. Basic notions 2 3

AN OVERVIEW OF SEPARATION AXIOMS IN RECENT RESEARCH
AN OVERVIEW OF SEPARATION AXIOMS IN RECENT RESEARCH

Introduction to Topology
Introduction to Topology

Surjective limits of locally convex spaces and their
Surjective limits of locally convex spaces and their

... holomorphy in locally convex spaces. In contrast to the other sections many of the proofs in this section have appeared previously [13]. We include this section, however, as some of the results are new (Example 4.7 and Proposition 4.8), some previous proofs have been simplified, and we are using a n ...

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.