Pointed Torsors

2011 ◽  
Vol 63 (6) ◽  
pp. 1345-1363
Author(s):  
J. F. Jardine
Keyword(s):  
Inverse Image ◽  
Profinite Group ◽  
Continuous Maps ◽  
Fundamental Groupoid ◽  
Geometric Morphism ◽  
Constant Group ◽  
Geometric Morphisms

AbstractThis paper gives a characterization of homotopy fibres of inverse image maps on groupoids of torsors that are induced by geometric morphisms, in terms of both pointed torsors and pointed cocycles, suitably defined. Cocycle techniques are used to give a complete description of such fibres, when the underlying geometric morphism is the canonical stalk on the classifying topos of a profinite group G. If the torsors in question are defined with respect to a constant group H, then the path components of the fibre can be identified with the set of continuous maps from the profinite group G to the group H. More generally, when H is not constant, this set of path components is the set of continuous maps from a pro-object in sheaves of groupoids to H, which pro-object can be viewed as a “Grothendieck fundamental groupoid”.

Minimal Sets on Graphs and Dendrites

2003 ◽  
Vol 13 (07) ◽  
pp. 1721-1725 ◽  
Author(s):  
Francisco Balibrea ◽  
Roman Hric ◽  
L'ubomír Snoha
Keyword(s):  
Topological Structure ◽  
Partial Characterization ◽  
Minimal Set ◽  
Full Characterization ◽  
Minimal Sets ◽  
Continuous Maps

The topological structure of minimal sets of continuous maps on graphs, dendrites and dendroids is studied. A full characterization of minimal sets on graphs and a partial characterization of minimal sets on dendrites are given. An example of a minimal set containing an interval on a dendroid is given.

On special operations on Ω-closeness on topological spaces

2015 ◽  
Vol 08 (03) ◽  
pp. 1550059
Author(s):  
S. A. Abd-El Baki ◽  
O. R. Sayed
Keyword(s):  
Topological Spaces ◽  
Special Operations ◽  
Closed Sets ◽  
Continuous Maps

In this paper, the concepts of [Formula: see text]-closed and [Formula: see text]-continuous maps are introduced and several properties of them are investigated. These concepts are used to obtain several results concerning the preservation of [Formula: see text]-closed sets. Moreover, we use [Formula: see text]-closed and [Formula: see text]-continuous maps to obtain a characterization of semi-[Formula: see text] spaces.

scholarly journals A CHARACTERIZATION OF THE SET Ω (f)\ ω (f) FOR CONTINUOUS MAPS OF THE INTERVAL WITH ZERO TOPOLOGICAL ENTROPY

1995 ◽  
Vol 05 (05) ◽  
pp. 1433-1435
Author(s):  
F. BALIBREA ◽  
J. SMÍTAL
Keyword(s):  
Topological Entropy ◽  
Minimal Set ◽  
Continuous Map ◽  
Continuous Maps ◽  
Limit Points ◽  
Infinite Set ◽  
Nonwandering Points

We give a characterization of the set of nonwandering points of a continuous map f of the interval with zero topological entropy, attracted to a single (infinite) minimal set Q. We show that such a map f can have a unique infinite minimal set Q and an infinite set B ⊂ Ω (f)\ ω (f) (of nonwandering points that are not ω-limit points) attracted to Q and such that B has infinite intersections with infinitely many disjoint orbits of f.

Automorphism groups of trivial strongly minimal structures

2003 ◽  
Vol 68 (2) ◽  
pp. 644-668
Author(s):  
Thomas Blossier
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Profinite Group ◽  
Hnn Extensions ◽  
Minimal Structure ◽  
Groups Of Automorphisms ◽  
Stabilizer Of A Point

AbstractWe study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group can be realized as the stabilizer of a point in a strongly minimal structure of bounded valency.

scholarly journals Degree 2 transformation semigroups as continuous maps on graphs: Foundations and structure

2021 ◽  
pp. 1-27
Author(s):  
Stuart Margolis ◽  
John Rhodes
Keyword(s):  
Graph Theory ◽  
Simple Semigroup ◽  
Semigroup Theory ◽  
Inverse Image ◽  
Transformation Semigroups ◽  
Partial Functions ◽  
Continuous Maps ◽  
Finite Set

We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elements. We show that the graph of fibers of such an action gives a deep connection between semigroup theory and graph theory. It is known that the Krohn–Rhodes complexity of a degree 2 action is at most 2. We show that the monoid of continuous maps on a graph is the translational hull of an appropriate 0-simple semigroup. We show how group mapping semigroups can be considered as regular covers of their right letter mapping image and relate this to their graph of fibers.

Categorical characterization of uniform hyperspaces

1983 ◽  
Vol 94 (2) ◽  
pp. 229-233 ◽  
Author(s):  
J. M. Harvey
Keyword(s):  
Uniform Spaces ◽  
Categorical Methods ◽  
Continuous Maps ◽  
Uniformly Continuous

In this paper, we use categorical methods to arrive at a characterization of Hausdorff hyperspaces of separated uniform spaces within a category of ordered uniform spaces. We begin by showing that the hyperspace construction gives rise to a monad H in the category Uni of non-empty separated uniform spaces and uniformly continuous maps. We then identify the category of H-algebras and characterize hyperspaces in this context.

Essential geometric morphisms between toposes over finite sets

1980 ◽  
Vol 87 (1) ◽  
pp. 21-24
Author(s):  
John Haigh
Keyword(s):  
Finite Sets ◽  
Generating Set ◽  
Cogenerating Set ◽  
Geometric Morphism ◽  
Geometric Morphisms

We show that if {Gi}J ε I is a generating set for an (elementary) topos ℰ then {P(Gi)}iεI is a cogenerating set for x2130;. From this we show that if topos ℰ contains an object G whose subobjects generate ℰ, then ΩG is a cogenerator for ℰ. Let denote the topos of finite sets and functions. We also show that if ℰ1 is a topos and ℰ2 is a bounded -topos then every geometric morphism ℰ1 → ℰ2 is essential.

scholarly journals Strongly algebraic = SFP (topically)

2001 ◽  
Vol 11 (6) ◽  
pp. 717-742 ◽  
Author(s):  
STEVEN VICKERS
Keyword(s):  
Information Systems ◽  
Geometric Theory ◽  
Upper Bounds ◽  
Finite Model ◽  
Finite Structure ◽  
Algebraic Domains ◽  
Finite Posets ◽  
Geometric Morphisms

Certain ‘Finite Structure Conditions’ on a geometric theory are shown to be sufficient for its classifying topos to be a presheaf topos. The conditions assert that every homomorphism from a finite structure of the theory to a model factors via a finite model, and they hold in cases where the finitely presentable models are all finite.The conditions are shown to hold for the theory of strongly algebraic (or SFP) information systems and some variants, as well as for some other theories already known to be classified by presheaf toposes.The work adheres to geometric constructivism throughout, and in consequence provides ‘topical’ categories of domains (internal in the category of toposes and geometric morphisms) with an analogue of Plotkin's double characterization of strongly algebraic domains, by sets of minimal upper bounds and by sequences of finite posets.

scholarly journals Neutrosophic e-Continuous Maps and Neutrosophic e-Irresolute Maps

2021 ◽  
Vol 12 (1S) ◽  
pp. 369-375
Author(s):  
A. Vadivel Et. al.
Keyword(s):  
Continuous Function ◽  
Topological Spaces ◽  
Properties And Characterization ◽  
Continuous Maps

Aim of this present paper is to introduce and investigate new kind of neutrosophic continuous function called neutrosophic econtinuous maps in neutrosophic topological spaces and also relate with their near continuous maps. Also, a new irresolute map called neutrosophic e-irresolute maps in neutrosophic topological spaces is introduced. Further, discussed about some properties and characterization of neutrosophic e-irresolute maps in neutrosophic topological spaces.

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