Set representations of abstract lattices
Set representations of abstract lattices

Nonnormality of Cech-Stone remainders of topological groups
Nonnormality of Cech-Stone remainders of topological groups

A NEW TOPOLOGY FROM AN OLD ONE Halgwrd Mohammed
A NEW TOPOLOGY FROM AN OLD ONE Halgwrd Mohammed

NOTE ON ⋆−CONNECTED IDEAL SPACES 1. Introduction and
NOTE ON ⋆−CONNECTED IDEAL SPACES 1. Introduction and

spaces of holomorphic functions and their duality
spaces of holomorphic functions and their duality

ON COVERING PROPERTIES BY REGULAR CLOSED SETS
ON COVERING PROPERTIES BY REGULAR CLOSED SETS

... answers a question posed by T. Noiri 15] whether rc-compactness is inversely preserved under continuous open perfect surjections. A different example answering Noiri's question is given in 21]. It is easily seen that rc-Lindelofness is preserved under continuous open surjections since under these ...
2.2 The Koopman representation
2.2 The Koopman representation

... subsets is an asymptotically invariant sequence if µ(En ∆γEn ) → 0, for all γ ∈ Γ. Such a sequence is said to be non-trivial if lim inf n→∞ µ(En )(1 − µ(En )) > 0. The action Γy(X, B, µ) is strongly ergodic if there does not exist a non-trivial asymptotically invariant sequence. Note that if Γy(X, B ...
On ωb-open sets and b
On ωb-open sets and b

An Introduction to Topology
An Introduction to Topology

F is ∀f ∈ F f(x) - Institut Camille Jordan
F is ∀f ∈ F f(x) - Institut Camille Jordan

Review of basic topology concepts
Review of basic topology concepts

On the category of topological topologies
On the category of topological topologies

Intersection homology
Intersection homology

o PAIRWISE LINDELOF SPACES
o PAIRWISE LINDELOF SPACES

pdf
pdf

Topology Definitions and Theorems Set Theory and Functions
Topology Definitions and Theorems Set Theory and Functions

Projective limits of topological vector spaces
Projective limits of topological vector spaces

arXiv:math/0110235v1 [math.AG] 21 Oct 2001
arXiv:math/0110235v1 [math.AG] 21 Oct 2001

Group Actions
Group Actions

SOME FIXED-POINT THEOREMS ON AN ALMOST G
SOME FIXED-POINT THEOREMS ON AN ALMOST G

FINITE TOPOLOGICAL SPACES 1. Introduction: finite spaces and
FINITE TOPOLOGICAL SPACES 1. Introduction: finite spaces and

... Theorem 2.13. The homeomorphism classes of finite spaces are in bijective correspondence with M . The number of sets in a minimal basis for X determines the size of the corresponding matrix, and the trace of the matrix is the number of elements of X. Proof. We work with minimal bases for the topolog ...
Continuous functions with compact support
Continuous functions with compact support

Metrizability of topological spaces
Metrizability of topological spaces

Continuity in Fine-Topological Space
Continuity in Fine-Topological Space

free topological groups with no small subgroups
free topological groups with no small subgroups

Covering space



In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.