ON A NOTION OF MAPS BETWEEN ORBIFOLDS I: FUNCTION SPACES

This is the first of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological structure of the space of such maps. In particular, we show that the space of such maps of Cr class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case. Motivations and applications of the theory come from string theory and the theory of pseudoholomorphic curves in symplectic orbifolds.

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Metric Spaces

10.1093/oso/9780192844507.003.0005 ◽

2021 ◽

pp. 103-125

Author(s):

James Davidson

Keyword(s):

Metric Space ◽

Metric Spaces ◽

Distance Measure ◽

Function Spaces ◽

Important Case ◽

General Context ◽

Compact Sets ◽

Definition Of ◽

Metric Distance

This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, examines the important case of function spaces, and treats the Arzelà–Ascoli theorem.

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I-Completeness in Function Spaces

Tatra Mountains Mathematical Publications ◽

10.2478/tmmp-2019-0017 ◽

2019 ◽

Vol 74 (1) ◽

pp. 35-46

Author(s):

Amar Kumar Banerjee ◽

Apurba Banerjee

Keyword(s):

Uniform Convergence ◽

Topological Structure ◽

Function Spaces ◽

Sufficient Condition

Abstract In this paper, we have studied the idea of ideal completeness of function spaces YX with respect to pointwise uniformity and uniformity of uniform convergence. Further, involving topological structure on X,wehaveobtained relationships between the uniformity of uniform convergence on compacta on YX and uniformity of uniform convergence on Y X in terms of I-Cauchy condition and I-convergence of a net. Also, using the notion of a k-space, we have given a sufficient condition for C(X, Y) to be ideal complete with respect to the uniformity of uniform convergence on compacta.

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The Creative Design of Injector Clamping Mechanism

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.418-420.2166 ◽

2011 ◽

Vol 418-420 ◽

pp. 2166-2169

Author(s):

Wan Chun Zhou ◽

Dong Min Liu

Keyword(s):

Topological Structure ◽

Kinematic Chain ◽

Kinematics And Dynamics ◽

Dynamics Analysis ◽

Connecting Rod ◽

Design Constraints ◽

Kinematic Chains ◽

Structure Characteristics ◽

Comprehensive Theory ◽

Design Requirements

Abstract. Analysis of a certain topological structure characteristics of clamping mechanism of injection machine, according to general principles, converts it into only containing Deputy General of the connecting rod and rotating chain. Bodies comprehensive theory of numbers after distribution combined with rod classes are general Atlas of kinematic chain. After identifying design constraints, on the redistribute members and turn the pair, you can get all man foot design requirements of viable specific Atlas of kinematic chains. Then every possible specific kinematic chain materialized to the schematic diagram of mechanism. Designers are on this basis through the kinematics and dynamics analysis to determine the best new clamping mechanism of injection machine.

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The Off-Screen

10.11126/stanford/9781503600720.001.0001 ◽

2017 ◽

Cited By ~ 2

Author(s):

Eyal Peretz

Keyword(s):

General Context ◽

Narrative Fiction ◽

Work Of Art ◽

American Cinema ◽

Modern Age ◽

Comprehensive Theory ◽

The Arts ◽

History Of ◽

General Meaning ◽

Modern Work

The Off-Screen offers a comprehensive theory of film, a concise history of American cinema from Griffith to Tarantino, and a reflection on the place and significance of film within the general context of the arts of modernity. It does this by focusing on an element at the very heart not only of film but of modern art in general (meaning here the various artistic media of modernity as they have been developed from the Renaissance onward). This element is a new kind of frame, with which the modern work of art is fascinated, and around the investigation of which it organizes itself. Two main things characterize this frame. First, it decontextualizes, meaning a frame is achieved by creating a zone that cuts itself off from the continuity of the world, a zone constituting the realm of fiction. The modern theatrical stage, the framed painting, the cinematic screen, the work of narrative fiction--all are modern framed-out zones. Second, the modern artistic frame, like any frame, creates a separation between “inside” and “outside,” yet the “outside” of the artistic frame is particularly mysterious and constitutes the main enigma of the work of art of the modern age. It is this “outside” of the artistic frame, a new kind of “outside,” that the book calls the “off” (as in off-stage, or off-screen). It is to the exploration of the historical and conceptual significance of this “off” that this book is dedicated.

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TOPOLOGICAL STRUCTURE IN $\hat c =1$ FERMIONIC STRING THEORY

Modern Physics Letters A ◽

10.1142/s0217732394002902 ◽

1994 ◽

Vol 09 (33) ◽

pp. 3077-3087 ◽

Cited By ~ 1

Author(s):

SHINJI HIRANO ◽

HIROSHI ISHIKAWA

Keyword(s):

String Theory ◽

Topological Structure ◽

Two Dimensions ◽

The Other ◽

Topological Model ◽

Enveloping Algebra ◽

Text String ◽

Physical Spectrum ◽

Fermionic String ◽

Mutually Independent

[Formula: see text] fermionic string theory, which is considered as a fermionic string theory in two dimensions, is shown to decompose into two mutually independent parts, one of which can be viewed as a topological model and the other is irrelevant for the theory. The physical contents of the theory is largely governed by this topological structure, and the discrete physical spectrum of [Formula: see text] string theory is naturally explained as the physical spectrum of the topological model. This topological structure turns out to be related with a novel hidden N = 2 superconformal algebra (SCA) in the enveloping algebra of the N = 3 SCA in fermionic string theories.

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