scholarly journals Notes on monotonically metacompact generalized ordered spaces

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ai-Jun Xu
Keyword(s):  
Generalized Ordered Space ◽  
Ordered Space

AbstractIn this paper, we show that any generalized ordered space X is monotonically (countably) metacompact if and only if the subspace X - { x } is monotonically (countably) metacompact for every point x of X and monotone (countable) metacompact property is hereditary with respect to convex (open) subsets in generalized ordered spaces. In addition, we show the equivalence of two questions posed by H.R. Bennett, K.P. Hart and D.J. Lutzer.

scholarly journals Dense Sδ-diagonals and linearly ordered extensions

2003 ◽  
Vol 4 (1) ◽  
pp. 71
Author(s):  
Masami Hosobuchi
Keyword(s):  
Topological Spaces ◽  
Generalized Ordered Space ◽  
Ordered Space

<p>The notion of the S<sub>δ</sub>-diagonal was introduced by H. R. Bennett to study the quasi-developability of linearly ordered spaces. In an earlier paper, we obtained a characterization of topological spaces with an S<sub>δ</sub>-diagonal and we showed that the S<sub>δ</sub>-diagonal property is stronger than the quasi-G<sub>δ</sub>-diagonal -diagonal property. In this paper, we define a dense S<sub>δ</sub>-diagonal of a space and show that two linearly ordered extensions of a generalized ordered space X have dense S<sub>δ</sub>-diagonals if the sets of right and left looking points are countable.</p>

scholarly journals The partially pre-ordered set of compactifications of Cp(X, Y)

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
A. Dorantes-Aldama ◽  
R. Rojas-Hernández ◽  
Á. Tamariz-Mascarúa
Keyword(s):  
Ordered Set ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
Countable Space ◽  
Generalized Ordered Space ◽  
Ordered Space ◽  
Countable Character ◽  
Corson Compact ◽  
First Countable Space ◽  
Isolated Point

AbstractIn the set of compactifications of X we consider the partial pre-order defined by (W, h) ≤X (Z, g) if there is a continuous function f : Z ⇢ W, such that (f ∘ g)(x) = h(x) for every x ∈ X. Two elements (W, h) and (Z, g) of K(X) are equivalent, (W, h) ≡X (Z, g), if there is a homeomorphism h : W ! Z such that (f ∘ g)(x) = h(x) for every x ∈ X. We denote by K(X) the upper semilattice of classes of equivalence of compactifications of X defined by ≤X and ≡X. We analyze in this article K(Cp(X, Y)) where Cp(X, Y) is the space of continuous functions from X to Y with the topology inherited from the Tychonoff product space YX. We write Cp(X) instead of Cp(X, R).We prove that for a first countable space Y, K(Cp(X, Y)) is not a lattice if any of the following cases happen:(a) Y is not locally compact,(b) X has only one non isolated point and Y is not compact.Furthermore, K(Cp(X)) is not a lattice when X satisfies one of the following properties:(i) X has a non-isolated point with countable character,(ii) X is not pseudocompact,(iii) X is infinite, pseudocompact and Cp(X) is normal,(iv) X is an infinite generalized ordered space.Moreover, K(Cp(X)) is not a lattice when X is an infinite Corson compact space, and for every space X, K(Cp(Cp(X))) is not a lattice. Finally, we list some unsolved problems.

scholarly journals A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY

2011 ◽  
Vol 83 (3) ◽  
pp. 463-469 ◽  
Author(s):  
YIN-ZHU GAO ◽  
WEI-XUE SHI
Keyword(s):  
Topological Space ◽  
List Type ◽  
Type Number ◽  
Projection Mapping ◽  
Ordered Topological Space ◽  
Linearly Ordered Topological Space ◽  
Generalized Ordered Space ◽  
Ordered Space

AbstractFor any generalized ordered space X with the underlying linearly ordered topological space Xu, let X* be the minimal closed linearly ordered extension of X and $\tilde {X}$ be the minimal dense linearly ordered extension of X. The following results are obtained. (1)The projection mapping π:X*→X, π(〈x,i〉)=x, is closed.(2)The projection mapping $\phi : \tilde {X} \rightarrow X_u$, ϕ(〈x,i〉)=x, is closed.(3)X* is a monotone D-space if and only if X is a monotone D-space.(4)$\tilde {X}$ is a monotone D-space if and only if Xu is a monotone D-space.(5)For the Michael line M, $\tilde {M}$ is a paracompact p-space, but not continuously Urysohn.

Scale, Landscape and Indigenous Bedouin Land Use: Spatial Order and Agricultural Sedentarisation in the Negev Highland

2021 ◽  
Vol 25 (1) ◽  
pp. 4-35
Author(s):  
Ariel Meraiot ◽  
Avinoam Meir ◽  
Steve Rosen
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Scale Analysis ◽  
Structure Development ◽  
British Mandate ◽  
Field Surveys ◽  
Ordered Field ◽  
Modern Period ◽  
Ordered Space ◽  
Sustainable Planning

By taking a small-scale perspective, Bedouin pastoral space in the Israeli Negev in the modern period has been misinterpreted as chaotic by various Israeli institutions. In critiquing this ontology we suggest that a knowledge gap with regard to an appropriate scale of understanding Bedouin settlement patterns and mechanisms of sedentarisation is at its root, and that a larger-scale analysis indicates that their space is in fact highly ordered. Field surveys and interviews with the local Bedouin showed that household cultivation plots in the Negev Highland during the period of the British Mandate were organised at a large scale through natural and man-made landscape features reflecting their structure, development and deployment in a highly ordered space. This analysis carries significant implications for understanding pastoral spaces at the local scale, particularly offering better comprehension of various sedentary forms and suggesting new approaches to sustainable planning and development for the Bedouin.

scholarly journals The pencil of the 4th and 3rd order surfaces obtained as a harmonic equivalent of the pencil of quadrics through a 4th order space curve of the 1st category

2012 ◽  
Vol 10 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Gordana Djukanovic ◽  
Marija Obradovic
Keyword(s):  
Cross Sections ◽  
Spatial Model ◽  
Spatial Models ◽  
Space Curve ◽  
Parabolic Cylinder ◽  
Triaxial Ellipsoid ◽  
Architectural Practice ◽  
Ordered Space ◽  
Pass Through ◽  
Frontal Projection

This paper shows the process of inverting the 4th ordered space curve of the first category with a self-intersecting point (with two planes of symmetry) and determining its harmonic equivalent. There are harmonic equivalents for five groups of surfaces obtained through the 4th order space curve of the 1st category. Mapping was done through a system of circular cross-sections. Both classical and relativistic geometry interpretations are presented. We also designed spatial models - a spatial model of the pencil of quadrics and a spatial model of the pencil of equivalent quadrics. Besides the boundary surfaces, one surface of the 3rd order, which is an equivalent to a triaxial ellipsoid, passes through this pencil of surface of the 4th order. The center of inversion is located on the contour of the ellipsoid. The parabolic cylinder is mapped into its equivalent, by mapping the contour parabola of the cylinder, in the frontal projection, in relation to the center and the sphere of inversion into a contour curve of the 4th order surface. The generating lines of the parabolic cylinder, which are in a projecting position and pass through the antipode, are mapped into circles (also in a projecting position) whose diameters are from the center of inversion to the contour line. The application of the 4th order surfaces in architectural practice is also presented.

scholarly journals A glance into the anatomy of monotonic maps

2021 ◽  
Vol 22 (1) ◽  
pp. 1
Author(s):  
Raushan Buzyakova
Keyword(s):  
Topological Space ◽  
Ordered Topological Space ◽  
Original Space ◽  
Ordered Space

<p>Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering. We note that the existence of such a re-ordering for a given map is equivalent to the map being conjugate (topologically equivalent) to a monotonic map on some homeomorphic ordered space. We observe that the latter cannot always be chosen to be order-isomorphic to the original space. Also, we identify other routes that may lead to similar affirmative statements for other classes of spaces and maps.</p>

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

A NONLINEAR EVOLUTION EQUATION IN AN ORDERED SPACE, ARISING FROM KINETIC THEORY

2007 ◽  
Vol 09 (02) ◽  
pp. 217-251
Author(s):  
CECIL P. GRÜNFELD
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Existence Theory ◽  
The Cauchy Problem ◽  
Ordered Space ◽  
Coagulation Equation ◽  
Boltzmann Model ◽  
Classical Boltzmann Equation

We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The analysis extends nontrivially monotonicity methods, originally developed in the context of the existence theory for the classical Boltzmann equation in L1. Our application examples are Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions, for which we obtain a unitary existence theory, with improved results, compared to the literature.

Electrodeposition of poly and nanocrystalline Cu-In-Se absorbers for optoelectronic devices

MRS Advances ◽  
2019 ◽  
Vol 4 (37) ◽  
pp. 2043-2052
Author(s):  
Shalini Menezes ◽  
Anura P. Samantilleke ◽  
Sharmila J. Menezes ◽  
Yi Mo ◽  
David S. Albin
Keyword(s):  
High Performance ◽  
Scale Up ◽  
Single Step ◽  
Light Emitting ◽  
3 Dimensional ◽  
Roll To Roll ◽  
Dimensional Network ◽  
Copper Indium ◽  
Ordered Space ◽  
Cu Foil

ABSTRACTCoupling semiconductors with electrochemical processes can lead to unusual materials, and attractive, practical device configurations. This work examines the reaction mechanism for single-step electrodeposition approach that creates device quality copper-indium-selenide (CISe) films with either polycrystalline or nanocrystalline morphologies on Cu and steel foils, respectively. The polycrystalline CISe film grows from In3+/Se4+ solution on Cu foil as Cu→ CuxSe→ CuInSe2; it may be used in standard planar pn devices. The nanocrystalline CISe film grown from Cu+/In3+/Se4+ solution follows the CuSe(In)→ CuInSe2→ CuIn3Se5 sequence. The latter approach leads to naturally ordered, space-filling nanocrystals, comprising interconnected 3-dimensional network of sharp, abrupt, p-CISe/n-CISe bulk homojunctions with extraordinary electro-optical attributes. Sandwiching these films between band-aligned contact electrodes can lead to high performance third generation devices for solar cells, light emitting diodes or photoelectrodes for fuel cells. Both approaches produce self-stabilized CISe absorbers that avoid recrystallization steps and can be roll-to-roll processed in simple flexible thin-film form factor for easy scale-up.

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