Images Of Class- Spaces

1973 ◽  
Vol 16 (3) ◽  
pp. 323-328
Author(s):  
Thomas W. Rishel
Keyword(s):  
Quotient Maps ◽  
Japan Acad ◽  
Almost Open ◽  
Open Maps

AbstractIn this paper the author characterizes images of class- spaces (as defined by Ishii, Tsuda and Kunugi, Proc. Japan Acad. 44, (1968), 897-903) under almost-open maps, bi-quotient maps, pseudoopen maps and quotient maps.

scholarly journals Almost locally connected spaces

1981 ◽  
Vol 31 (4) ◽  
pp. 421-428 ◽  
Author(s):  
Vincent J. Mancuso
Keyword(s):  
Connected Space ◽  
Local Connectedness ◽  
Quotient Maps ◽  
Regular Open ◽  
Connected Spaces ◽  
Open Maps

AbstractThis paper introduces the concept of an almost locally connected space. Every locally connected space is almost locally connected, and the concepts are equivalent in the class of semi-regular spaces. Almost local connectedness is hereditary for regular open subspaces, is preserved by continuous open maps, but not generally by quotient maps. It is productive in the presence of almost-regularity.

scholarly journals Characterizations of some near-continuous functions and near-open functions

1986 ◽  
Vol 9 (4) ◽  
pp. 715-720 ◽  
Author(s):  
C. W. Baker
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Open Set ◽  
Weakly Continuous ◽  
Almost Open ◽  
Open Maps

A subsetNof a topological space is defined to be aθ-neighborhood ofxif there exists an open setUsuch thatx∈U⫅C1   U⫅N. This concept is used to characterize the following types of functions: weakly continuous,θ-continuous, stronglyθ-continuous, almost stronglyθ-continuous, weaklyδ-continuous, weakly open and almost open functions. Additional characterizations are given for weaklyδ-continuous functions. The concept ofθ-neighborhood is also used to define the following types of open maps:θ-open, stronglyθ-open, almost stronglyθ-open, and weaklyδ-open functions.

Certain new kinds of αrps - open maps in topological spaces

2021 ◽  
pp. 1-8
Author(s):  
Dunya Mohamed Hameed ◽  
Intidhar Zamil Mushtt ◽  
Shimaa Mohammed Dawood
Keyword(s):  
Topological Spaces ◽  
Open Maps

On topological quotient maps preserved by pullbacks or products

1970 ◽  
Vol 67 (3) ◽  
pp. 553-558 ◽  
Author(s):  
B. J. Day ◽  
G. M. Kelly
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Quotient Maps ◽  
Continuous Maps

We are concerned with the category of topological spaces and continuous maps. A surjection f: X → Y in this category is called a quotient map if G is open in Y whenever f−1G is open in X. Our purpose is to answer the following three questions:Question 1. For which continuous surjections f: X → Y is every pullback of f a quotient map?Question 2. For which continuous surjections f: X → Y is f × lz: X × Z → Y × Z a quotient map for every topological space Z? (These include all those f answering to Question 1, since f × lz is the pullback of f by the projection map Y ×Z → Y.)Question 3. For which topological spaces Z is f × 1Z: X × Z → Y × Z a qiptoent map for every quotient map f?

A note on semi-open and almost open induced maps

2021 ◽  
pp. 107823
Author(s):  
Alvaro Andrade ◽  
Javier Camargo
Keyword(s):  
Almost Open ◽  
Induced Maps

scholarly journals In Silico Evolution of Early Metabolism

2011 ◽  
Vol 17 (2) ◽  
pp. 87-108 ◽  
Author(s):  
Alexander Ullrich ◽  
Markus Rohrschneider ◽  
Gerik Scheuermann ◽  
Peter F. Stadler ◽  
Christoph Flamm
Keyword(s):  
Metabolic Pathways ◽  
Genetic System ◽  
Simulation Tool ◽  
Metabolic Evolution ◽  
Metabolic System ◽  
Evolution Of Metabolic Pathways ◽  
Core Set ◽  
Catalytically Active ◽  
Almost Open ◽  
In Silico Evolution

We developed a simulation tool for investigating the evolution of early metabolism, allowing us to speculate on the formation of metabolic pathways from catalyzed chemical reactions and on the development of their characteristic properties. Our model consists of a protocellular entity with a simple RNA-based genetic system and an evolving metabolism of catalytically active ribozymes that manipulate a rich underlying chemistry. Ensuring an almost open-ended and fairly realistic simulation is crucial for understanding the first steps in metabolic evolution. We show here how our simulation tool can be helpful in arguing for or against hypotheses on the evolution of metabolic pathways. We demonstrate that seemingly mutually exclusive hypotheses may well be compatible when we take into account that different processes dominate different phases in the evolution of a metabolic system. Our results suggest that forward evolution shapes metabolic network in the very early steps of evolution. In later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a core set of pathways from the early phase.

scholarly journals Bisimulation from Open Maps

1994 ◽  
Vol 1 (7) ◽  
Author(s):  
André Joyal ◽  
Mogens Nielsen ◽  
Glynn Winskel
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Transition Systems ◽  
New Model ◽  
Event Structures ◽  
Uniform Definition ◽  
Refinement Operators ◽  
Definition Of ◽  
Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

scholarly journals A Presheaf Semantics of Value-Passing Processes

1996 ◽  
Vol 3 (44) ◽  
Author(s):  
Glynn Winskel
Keyword(s):  
Operational Semantics ◽  
Denotational Semantics ◽  
Domain Theory ◽  
Process Calculi ◽  
Traditional Definition ◽  
Open Maps

This paper investigates presheaf models for process calculi with<br />value passing. Denotational semantics in presheaf models are shown<br />to correspond to operational semantics in that bisimulation obtained<br />from open maps is proved to coincide with bisimulation as defined<br />traditionally from the operational semantics. Both "early" and "late"<br />semantics are considered, though the more interesting "late" semantics<br />is emphasised. A presheaf model and denotational semantics is proposed<br />for a language allowing process passing, though there remains<br />the problem of relating the notion of bisimulation obtained from open<br />maps to a more traditional definition from the operational semantics.<br />A tentative beginning is made of a "domain theory" supporting<br />presheaf models.

scholarly journals On R#-Closed and R#-Open Maps in Topological Spaces

2018 ◽  
Vol 7 (4.10) ◽  
pp. 770
Author(s):  
Raghavendra K ◽  
Basavaraj M. Ittanagi
Keyword(s):  
Topological Spaces ◽  
Open Maps

Defining and investigating properties of R#-closed maps, R#-open maps, R#*-closed maps and R#*-open maps in topological spaces.2010 Mathematics Classification: 54A05, 54A10 

scholarly journals A Representation Result for Free Cocompletions

1998 ◽  
Vol 5 (21) ◽  
Author(s):  
John Power ◽  
Gian Luca Cattani ◽  
Glynn Winskel
Keyword(s):  
Small Category ◽  
Representation Result ◽  
Open Maps ◽  
Class F

Given a class F of weights, one can consider the construction that<br />takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F. Provided these free Fcocompletions are small, this construction generates a 2-monad on Cat, or more generally on V-Cat for monoidal biclosed complete and cocomplete V. We develop the notion of a dense 2-monad on V-Cat and characterise free F-cocompletions by dense KZ-monads on V-Cat. We prove various corollaries about the structure of such 2-monads and their Kleisli 2-categories, as needed for the use of open maps in giving an axiomatic study of bisimulation in concurrency. This requires the introduction of the concept of a pseudo-commutativity for a strong 2-monad on a symmetric monoidal 2-category, and a characterisation of it in terms of structure on the Kleisli 2-category.

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