a hit-and-miss hyperspace topology on the space of fuzzy sets
a hit-and-miss hyperspace topology on the space of fuzzy sets

SOME UNIVERSALITY RESULTS FOR
SOME UNIVERSALITY RESULTS FOR

Compact Orthoalgebras - Susquehanna University
Compact Orthoalgebras - Susquehanna University

MAPPING STACKS OF TOPOLOGICAL STACKS Contents 1
MAPPING STACKS OF TOPOLOGICAL STACKS Contents 1

A Demonstration that Quotient Spaces of Locally Compact Hausdorff
A Demonstration that Quotient Spaces of Locally Compact Hausdorff

A NOTE ON PRE
A NOTE ON PRE

MAPPING STACKS OF TOPOLOGICAL STACKS
MAPPING STACKS OF TOPOLOGICAL STACKS

Locally compact groups and continuous logic
Locally compact groups and continuous logic

Set Theory
Set Theory

normed linear spaces of continuous functions
normed linear spaces of continuous functions

... Obviously (3) ' enables us to use the Stone-Weierstrass approximation theorem. Clarkson's solution [ó] of the problem of characterizing B(X) consists essentially of condition (2)', together with the demand that the half cone in B with vertex e and directrix E has the property that the intersection o ...
RADON-NIKOD´YM COMPACT SPACES OF LOW WEIGHT AND
RADON-NIKOD´YM COMPACT SPACES OF LOW WEIGHT AND

Remarks concerning the invariance of Baire spaces under mappings
Remarks concerning the invariance of Baire spaces under mappings

CONTRA-CONTINUOUS FUNCTIONS AND STRONGLY S
CONTRA-CONTINUOUS FUNCTIONS AND STRONGLY S

QUASIGROÜPS. I
QUASIGROÜPS. I

DIRECT LIMITS, INVERSE LIMITS, AND PROFINITE GROUPS The
DIRECT LIMITS, INVERSE LIMITS, AND PROFINITE GROUPS The

... so in Grp), Rng of rings, and R-Mod of modules over a given ring R. Proof. The construction of the inverse limit in each of these categories is the same, and so we just look at the category of topological groups. Let {Gi }i∈I be a collection of topological groups indexed by the directed set i ∈ I, a ...
On α-normal and β-normal spaces
On α-normal and β-normal spaces

CHARACTERIZING CONTINUITY BY PRESERVING
CHARACTERIZING CONTINUITY BY PRESERVING

S -paracompactness in ideal topological spaces
S -paracompactness in ideal topological spaces

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

minimal sequential hausdorff spaces
minimal sequential hausdorff spaces

Mappings and realcompact spaces
Mappings and realcompact spaces

Topological constructors
Topological constructors

F A S C I C U L I M A T H E M A T I C I
F A S C I C U L I M A T H E M A T I C I

4. Sheaves Definition 4.1. Let X be a topological space. A presheaf
4. Sheaves Definition 4.1. Let X be a topological space. A presheaf

Remarks on neighborhood star-Lindel¨of spaces II
Remarks on neighborhood star-Lindel¨of spaces II

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.