BORNOLOGICAL CONVERGENCES A. Lechicki, S. Levi, and A
BORNOLOGICAL CONVERGENCES A. Lechicki, S. Levi, and A

Topological and Limit-space Subcategories of Countably
Topological and Limit-space Subcategories of Countably

MONADS AND ALGEBRAIC STRUCTURES Contents 1
MONADS AND ALGEBRAIC STRUCTURES Contents 1

T-Spaces - Tubitak Journals
T-Spaces - Tubitak Journals

subgroups of free topological groups and free
subgroups of free topological groups and free

Baire Measures and its Unique Extension to a Regular Boral Measure
Baire Measures and its Unique Extension to a Regular Boral Measure

Monoidal closed, Cartesian closed and convenient categories of
Monoidal closed, Cartesian closed and convenient categories of

Old Lecture Notes (use at your own risk)
Old Lecture Notes (use at your own risk)

generalized topological vector subspaces
generalized topological vector subspaces

HAUSDORFF TOPOLOGIES ON GROUPS
HAUSDORFF TOPOLOGIES ON GROUPS

EBERLEIN–ŠMULYAN THEOREM FOR ABELIAN TOPOLOGICAL
EBERLEIN–ŠMULYAN THEOREM FOR ABELIAN TOPOLOGICAL

... Proposition 2. If X is an angelic space, then it is a g + IN + Š-space. We will see below that angelic spaces have quite good stability properties; nevertheless, the product of two angelic spaces may not be angelic. This fact motivated Govaerts [16] to define the strictly angelic spaces as those ang ...
Metric Spaces
Metric Spaces

Topological ordered spaces as a foundation for a quantum
Topological ordered spaces as a foundation for a quantum

An Introduction to Topology
An Introduction to Topology

General Topology of Ramified Coverings
General Topology of Ramified Coverings

Metric Spaces in Synthetic Topology
Metric Spaces in Synthetic Topology

... Proof: Take U ⊆ Y open. As f is continuous, f −1 (U) is open, hence metric open in X. Since f is a metric open surjection, U = f (f −1 (U)) is metric open in Y. ...
On topologies defined by irreducible sets
On topologies defined by irreducible sets

CONNECTIVE SPACES 1. Connective Spaces 1.1. Introduction. As
CONNECTIVE SPACES 1. Connective Spaces 1.1. Introduction. As

homotopy types of topological stacks
homotopy types of topological stacks

... one to transport homotopical information back and forth between the diagram and its homotopy type. The above theorem has various applications. For example, it implies an equivariant version of Theorem 1.1 for the (weak) action of a discrete group. It also allows one to define homotopy types of pairs ...
Introduction to Quad topological spaces(4-tuple topology)
Introduction to Quad topological spaces(4-tuple topology)

Zero-pointed manifolds
Zero-pointed manifolds

TOPOLOGY PROCEEDINGS
TOPOLOGY PROCEEDINGS

... We give here a self-contained and unified exposition of some new and old results around two problems (A) and (B) mentioned above. We obtain several results which concentrate on similarities between group and semigroup cases. On the other hand we give also relevant contrasting counterexamples. 2. Mai ...
FELL BUNDLES ASSOCIATED TO GROUPOID MORPHISMS §1
FELL BUNDLES ASSOCIATED TO GROUPOID MORPHISMS §1

... and prove a structure theorem that states that every such bundle arises from a twisted groupoid covering. We also give various examples of abelian Fell bundles and an application of the structure theorem. §2. FELL BUNDLES OVER GROUPOIDS Recall the definition of a Fell bundle over a groupoid G (see [ ...
Introduction to spectral spaces
Introduction to spectral spaces

Connectedness in fuzzy topology
Connectedness in fuzzy topology

Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical. They exist in several varieties such as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets.There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of them, are essential parts of sheaf theory.Due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry. First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the ""usual"" topological cohomology theories such as singular cohomology. Especially in algebraic geometry and the theory of complex manifolds, sheaf cohomology provides a powerful link between topological and geometric properties of spaces. Sheaves also provide the basis for the theory of D-modules, which provide applications to the theory of differential equations. In addition, generalisations of sheaves to more general settings than topological spaces, such as Grothendieck topology, have provided applications to mathematical logic and number theory.