Cartan-Whitehead decomposition as Adams cocompletion

1987 ◽  
Vol 42 (2) ◽  
pp. 223-226 ◽  
Author(s):  
A. Behera ◽  
S. Nanda
Keyword(s):  
Connected Space ◽  
Dual Notion

AbstractDeleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, the Adams cocompletion of an object in a category. In this paper the different stages of the Cartan-Whitehead decomposition of a 0-connected space are shown to be the cocompletions of the space with respect to suitable sets of morphisms.

Causal-Consistent Replay Reversible Semantics for Message Passing Concurrent Programs

2021 ◽  
Vol 178 (3) ◽  
pp. 229-266
Author(s):  
Ivan Lanese ◽  
Adrián Palacios ◽  
Germán Vidal
Keyword(s):  
Programming Language ◽  
Message Passing ◽  
Concurrent Programming ◽  
Concurrent Systems ◽  
Concurrent Programs ◽  
Unified Framework ◽  
Innovative Technique ◽  
Dual Notion

Causal-consistent reversible debugging is an innovative technique for debugging concurrent systems. It allows one to go back in the execution focusing on the actions that most likely caused a visible misbehavior. When such an action is selected, the debugger undoes it, including all and only its consequences. This operation is called a causal-consistent rollback. In this way, the user can avoid being distracted by the actions of other, unrelated processes. In this work, we introduce its dual notion: causal-consistent replay. We allow the user to record an execution of a running program and, in contrast to traditional replay debuggers, to reproduce a visible misbehavior inside the debugger including all and only its causes. Furthermore, we present a unified framework that combines both causal-consistent replay and causal-consistent rollback. Although most of the ideas that we present are rather general, we focus on a popular functional and concurrent programming language based on message passing: Erlang.

scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

scholarly journals THE DUAL NOTION OF MULTIPLICATION MODULES

2007 ◽  
Vol 11 (4) ◽  
pp. 1189-1201 ◽  
Author(s):  
H. Ansari-Toroghy ◽  
F. Farshadifar
Keyword(s):  
Dual Notion

Mutual Determination, Concrescence and Transition. Whitehead’s Speculative Conception of Temporal Subjectivity Interpreted from a Merleau-Pontyan Standpoint

2020 ◽  
Vol 22 ◽  
pp. 101-117
Author(s):  
Luca Vanzago ◽  
Keyword(s):  
Mathematical Concepts ◽  
Material World ◽  
Natural Knowledge ◽  
Constant Change ◽  
Interpretive Approach ◽  
Dual Notion ◽  
Mathematics And Physics ◽  
Processual Approach

The interpretive approach adopted in this paper is influenced by Merleau-Ponty’s philosophy and in particular by his understanding of Nature, which in turn takes into consideration Whitehead’s work. Whitehead’s philosophy of organism is seen by its author as the metaphysical generalization of problems found in his investigation of natural knowledge. Whitehead admits that a speculative approach is necessitated by the very questions arising from the mathematical concepts of the material world and the revolutions undergone in logic, mathematics and physics at the turn of the century.Whitehead’s understanding of nature is framed from the beginning in terms of a processual approach. However, this notion of process is not fully worked out in the epistemological works and requires a metaphysical deepening. This is due to the fact that the notion of duration adopted in the epistemological works is not sufficient to convey the notion of process. This lack of adequacy is coupled by Whitehead with the need to interpret process in terms of experience. In turn, this notion of experience is wider than the usual one, for it implies that there is experience from the lowest levels onwards. Matter itself experiences. Seen in this perspective, reality is thus conceived in terms of a whole in constant change, whose parts are in mutual connection. This conception derives from Whitehead’s criticism of Aristotle’s substantialism and from his preference for a relationist ontology. The outcome of this approach is a speculative conception of reality in terms of a twofold notion of process: concrescence and transition, which Whitehead sees as the two faces of the creative advance of nature. This dual notion of process is interpreted in this essay in a merleau-pontyan perspective.

scholarly journals New types of locally connected spaces via clopen set

2021 ◽  
Vol 40 (3) ◽  
pp. 671-679
Author(s):  
Ennis Rafael Rosas Rodríguez ◽  
Sarhad F. Namiq
Keyword(s):  
Connected Space ◽  
New Type ◽  
Connected Spaces

In this paper, we define and study a new type of connected spaces called λco-connected space. It is remarkable that the class of λ-connected spaces is a subclass of the class of λco-connected spaces. We discuss some characterizations and properties of λco-connected spaces, λco components and λco-locally connected spaces

scholarly journals Diagonals of separately continuous maps with values in box products

2018 ◽  
Vol 6 (1) ◽  
pp. 26-33
Author(s):  
Olena Karlova ◽  
Volodymyr Mykhaylyuk
Keyword(s):  
Connected Space ◽  
Continuous Map ◽  
Continuous Maps ◽  
Baire One ◽  
Metrizable Spaces

Abstract We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such that f (x, x) = g(x) for all x ∈ X.

Notizen: On Chiral Symmetry Breaking in a Non-Simply Connected Space-Time

1985 ◽  
Vol 40 (9) ◽  
pp. 957-958
Author(s):  
Pinaki Roy ◽  
Rajkumar Roychoudhury
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Space Time ◽  
Connected Space ◽  
Global Space ◽  
Simply Connected

Abstract We consider QCD in R3 x S1 and show that non-trivial global space-time topology breaks chiral symmetry.

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