Shape morphisms and components of movable compacta

1988 ◽  
Vol 103 (3) ◽  
pp. 481-486
Author(s):  
José M. R. Sanjurjo
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
The Other ◽  
Compact Metric Space ◽  
Dimension Zero ◽  
Compact Metric Spaces ◽  
Inductive Dimension ◽  
Other Hand ◽  
Small Inductive Dimension ◽  
The Relationship

The relationship between components and movability for compacta (i.e. compact metric spaces) was described by Borsuk in [5]. Borsuk proved that if each component of a compactum X is movable, then so is X. More recently Segal and Spiez[19], motivated by results of Alonso Morón[1], have constructed a (non-compact) metric space X of small inductive dimension zero and such that X is non-movable. The construction of Segal and Spiez was based on the famous space of P. Roy [16]. On the other hand, K. Borsuk gave in [5] an example of a movable compactum with non-movable components. The structure of such compacta was studied by Oledzki in [15], where he obtained an interesting result stating that if X is a movable compactum then the set of movable components of X is dense in the space of components of X. Oledzki's result was later strengthened by Nowak[14], who proved that if all movable components of a movable compactum X are of deformation dimension at most n, then so are the non-movable components and the compactum X itself.

scholarly journals ON BUCK’S UNIFORM DISTRIBUTION IN COMPACT METRIC SPACES

2013 ◽  
Vol 56 (1) ◽  
pp. 61-66
Author(s):  
Milan Paštéka
Keyword(s):  
Uniform Distribution ◽  
Metric Space ◽  
Existence Result ◽  
Metric Spaces ◽  
Theoretic Approach ◽  
Compact Metric Space ◽  
Compact Metric Spaces

ABSTRACT We define uniform distribution in compact metric space with respect to the Buck’s measure density originated in [Buck, R. C.: The measure theoretic approach to density, Amer. J. Math. 68 (1946), 560-580]. Weyl’s criterion is derived. This leads to an existence result.

scholarly journals Fuzzy b-Metric Spaces

2016 ◽  
Vol 11 (2) ◽  
pp. 273 ◽  
Author(s):  
Sorin Nădăban
Keyword(s):  
Control Theory ◽  
Computer Science ◽  
Metric Space ◽  
Metric Spaces ◽  
Denotational Semantics ◽  
Decomposition Theorem ◽  
The Other ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
Other Hand

Metric spaces and their various generalizations occur frequently in computer science applications. This is the reason why, in this paper, we introduced and studied the concept of fuzzy b-metric space, generalizing, in this way, both the notion of fuzzy metric space introduced by I. Kramosil and J. Michálek and the concept of b-metric space. On the other hand, we introduced the concept of fuzzy quasi-bmetric space, extending the notion of fuzzy quasi metric space recently introduced by V. Gregori and S. Romaguera. Finally, a decomposition theorem for a fuzzy quasipseudo- b-metric into an ascending family of quasi-pseudo-b-metrics is established. The use of fuzzy b-metric spaces and fuzzy quasi-b-metric spaces in the study of denotational semantics and their applications in control theory will be an important next step.

Decomposition Space Theory and the Bing Shrinking Criterion

2021 ◽  
pp. 62-76
Author(s):  
Christopher W. Davis ◽  
Boldizsár Kalmár ◽  
Min Hoon Kim ◽  
Henrik Rüping
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Embedding Theorem ◽  
Space Theory ◽  
Compact Metric Space ◽  
Decomposition Spaces ◽  
Compact Metric Spaces ◽  
Space Decomposition ◽  
Decomposition Space ◽  
Continuous Decomposition

‘Decomposition Space Theory and the Bing Shrinking Criterion’ gives a proof of the central Bing shrinking criterion and then provides an introduction to the key notions of the field of decomposition space theory. The chapter begins by proving the Bing shrinking criterion, which characterizes when a given map between compact metric spaces is approximable by homeomorphisms. Next, it develops the elements of the theory of decomposition spaces. A key fact is that a decomposition space associated with an upper semi-continuous decomposition of a compact metric space is again a compact metric space. Decomposition spaces are key in the proof of the disc embedding theorem.

scholarly journals Generalized Lipschitz Algebras

1969 ◽  
Vol 12 (1) ◽  
pp. 1-19 ◽  
Author(s):  
E.R. Bishop
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Compact Metric Spaces ◽  
Continuous Maps ◽  
The Relationship

The purpose of this paper is to generalize the results of Sherbert on Lipschitz algebras and to study the relationship between homomorphisms of these algebras and continuous maps of the underlying metric spaces. In Sections 1, 2, and 3 we associate with each metric space a class of Lipschitz-type algebras and extend Sherbert's results in [7] to this class; in particular Sherbert's theorem 5.1 is extended to non-compact metric spaces (3.3, 3.4, 3.5).

scholarly journals A theorem on homeomorphism groups and products of spaces

1969 ◽  
Vol 1 (1) ◽  
pp. 137-141 ◽  
Author(s):  
A. R. Vobach
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Structure Theorem ◽  
Cantor Set ◽  
Compact Metric Space ◽  
Compact Metric Spaces ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

Let H(C) be the group of homeomorphisms of the Cantor set, C, onto itself. Let p: C → M be a map of C onto a compact metric space M, and let G(p, M) be is a group.The map p: C → M is standard, if for each (x, y) ∈ C × C such that p(x) = p(y), there is a sequence and a sequence such that xn → x and hn (xn) → y Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N, are homeomorphic if and only if, given p standard from C onto M, there is a standard q from C onto N for which G(p, M) = h−1G(q, N)h, for some h ∈ H(C) The present paper exhibits a structure theorem connecting these characterizing subgroups of H(C) and products of spaces: Let M1 and M2 be compact metric spaces. Then there are standard maps p: C → M1 × M2 and pi: C → Mi, i = 1, 2, such that G(p, M1 × M2) = G(p1, M1) ∩ G(p2, M2).

Some properties of positive entropy maps

2013 ◽  
Vol 34 (3) ◽  
pp. 765-776 ◽  
Author(s):  
A. ARBIETO ◽  
C. A. MORALES
Keyword(s):  
Invariant Measure ◽  
Metric Space ◽  
Metric Spaces ◽  
Acta Math ◽  
Positive Entropy ◽  
Canonical Coordinates ◽  
Compact Metric Space ◽  
Compact Metric Spaces ◽  
Positive Topological Entropy ◽  
Continuous Map

AbstractWe prove that the stable classes for continuous maps on compact metric spaces have measure zero with respect to any ergodic invariant measure with positive entropy. Then, every continuous map with positive topological entropy on a compact metric space has uncountably many stable classes. We also prove that every continuous map with positive topological entropy of a compact metric space cannot be Lyapunov stable on its recurrent set. For homeomorphisms on compact metric spaces we prove that the sets of heteroclinic points, and sinks in the canonical coordinates case, have zero measure with respect to any ergodic invariant measure with positive entropy. These results generalize those of Fedorenko and Smital [Maps of the interval Ljapunov stable on the set of nonwandering points. Acta Math. Univ. Comenian. (N.S.)60 (1) (1991), 11–14], Huang and Ye [Devaney’s chaos or 2-scattering implies Li–Yorke’s chaos. Topology Appl.117 (3) (2002), 259–272], Reddy [The existence of expansive homeomorphisms on manifolds. Duke Math. J.32 (1965), 627–632], Reddy and Robertson [Sources, sinks and saddles for expansive homeomorphisms with canonical coordinates. Rocky Mountain J. Math.17 (4) (1987), 673–681], Sindelarova [A counterexample to a statement concerning Lyapunov stability. Acta Math. Univ. Comenian. 70 (2001), 265–268], and Zhou [Some equivalent conditions for self-mappings of a circle. Chinese Ann. Math. Ser. A12(suppl.) (1991), 22–27].

‘He Brought the Cold Death on my Harandra’: The Cosmic Trilogy and the Ecotheology of Laudato si'

2018 ◽  
Vol 8 (2) ◽  
pp. 166-182
Author(s):  
Maria Poggi Johnson
Keyword(s):  
Natural Environment ◽  
The Other ◽  
Space Travel ◽  
Human Relationships ◽  
Other Hand ◽  
Divine Will ◽  
The Relationship

In his trilogy of space travel novels, published between 1938 and 1945, C.S. Lewis strikingly anticipates, and incarnates in imaginative form, the insights and concerns central to the modern discipline of ecotheology. The moral and spiritual battle that forms the plot of the novels is enacted and informed by the relationship between humans and the natural environment, Rebellion against, and alienation from, the Creator inevitably manifests in a violent and alienated attitude to creation, which is seen as something to be mastered and exploited. Lives and cultures in harmony with the divine will, on the other hand, are expressed in relationships of care and respect for the environment. The imaginative premise of the Trilogy is that of ecotheology; that the human relationships with God, neighbour, and earth and are deeply and inextricably intertwined.

KONSTRUKSI ISLAM DALAM KEKUASAAN NEGARA

1970 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurul Aini Musyarofah
Keyword(s):  
Islamic Law ◽  
Social Condition ◽  
The Other ◽  
Good Society ◽  
Ideal Form ◽  
Other Hand ◽  
Islamic Politics ◽  
The Relationship ◽  
The Ideal

The relationship between Islam and state raises a controversy that includes two main groups;formalists and substantialists. Both of them intend to achieve a good social condition which is inaccordance with Islamic politics. The ideal form of good society to be achieved is principallydescribed in the main source of Islamic law, Al Qur’an and As Sunnah, as follows. A form of goodsociety should supprot equality and justice, egalitarianism, and democracy in its social community.The next problem is what the needed methods and instruments to achieve the ideal Islamic politicsare. In this case, the debate on the formalization and substance of Islamic teaching is related to therunning formal political institution.Each group claims itself to be the most representative to the ideal Islam that often leads to anescalating conflict. On the other hand thr arguments of both groups does not reach the wholeMuslims. As a result, the discourse of Islam and state seems to be elitist and political. As a result,Both groups suspect each other each other and try to utilize the controversy on the relationshipbetween Islam and state to get their own benefit which has no relation with the actualization ofIslamic teaching.

8. ADMINISTRASI HUSEMAS

2020 ◽  
Author(s):  
putri asifa ◽  
Hade Afriansyah
Keyword(s):  
School Improvement ◽  
Educational Needs ◽  
The Other ◽  
Community Interest ◽  
Other Hand ◽  
School And Community ◽  
The Relationship

This article discusses the administration of school and community relation. The existence of schools is driven by the needs of the community, because educational responsibilities are governed by the responsibilities of the community, family, and government. Based on these relationships, the relationship is always enhanced. But something is seen. Changes in nature, goals, and methods of teaching relationships. On the other hand, the community also demands the change in education. In Indonesia, the relationship between schools and the community has been established. This is good progress.Therefore, Husemas is a process of communication between schools and the community to increase community understanding of educational needs and activities and encourage community interest and cooperation in school improvement and development.

scholarly journals From reflex to reflection: Moving from the space of causes to the space of reasons and back

2020 ◽  
Vol 3 (1) ◽  
pp. 681-693
Author(s):  
Ariel Furstenberg
Keyword(s):  
The Other ◽  
Final Part ◽  
Clear Cut ◽  
Other Hand ◽  
Space Of Reasons ◽  
The One ◽  
The Relationship ◽  
Simple Picture

AbstractThis article proposes to narrow the gap between the space of reasons and the space of causes. By articulating the standard phenomenology of reasons and causes, we investigate the cases in which the clear-cut divide between reasons and causes starts to break down. Thus, substituting the simple picture of the relationship between the space of reasons and the space of causes with an inverted and complex one, in which reasons can have a causal-like phenomenology and causes can have a reason-like phenomenology. This is attained by focusing on “swift reasoned actions” on the one hand, and on “causal noisy brain mechanisms” on the other hand. In the final part of the article, I show how an analogous move, that of narrowing the gap between one’s normative framework and the space of reasons, can be seen as an extension of narrowing the gap between the space of causes and the space of reasons.

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