scholarly journals Density topologies on the plane between ordinary and strong

2009 ◽  
Vol 44 (1) ◽  
pp. 139-151
Author(s):  
Elžbieta Wagner-Bojakowska ◽  
Władysław Wilczyński
Keyword(s):  
Measurable Subset ◽  
Continuous Functions ◽  
Density Point ◽  
Density Topology ◽  
Starting Point ◽  
The Family

Abstract Let C0 denote the set of all non-decreasing continuous functions f : (0, 1] →(0, 1] such that limx→0+ ƒ(x) = 0 and ƒ(x) ≤ x for x ∈(0, 1] and let A be a measurable subset of the plane. We define the notion of a density point of A with respect to ƒ. This is a starting point to introduce the mapping Dƒ defined on the family of all measurable subsets of the plane, which is so-called lower density. The mapping Dƒ leads to the topology Tƒ, analogously as for the density topology. The properties of the topologies Tƒ are considered.

scholarly journals Density topologies on the plane between ordinary and strong. II

2015 ◽  
Vol 62 (1) ◽  
pp. 13-25
Author(s):  
Elżbieta Wagner-Bojakowska ◽  
Władysław Wilczyński
Keyword(s):  
Topological Space ◽  
Measurable Subset ◽  
Continuous Functions ◽  
Density Point ◽  
Density Topology ◽  
Completely Regular ◽  
The Family

Abstract Let C0 denote a set of all non-decreasing continuous functions f : (0, 1] → (0, 1] such that limx→0+f(x) = 0 and f(x) ≤ x for every x ∊ (0, 1], and let A be a measurable subset of the plane. The notions of a density point of A with respect to f and the mapping defined on the family of all measurable subsets of the plane were introduced in Wagner-Bojakowska, E. Wilcziński, W.: Density topologies on the plane between ordinary and strong, Tatra Mt. Math. Publ. 44 (2009), 139 151. This mapping is a lower density, so it allowed us to introduce the topology Tf , analogously to the density topology. In this note, properties of the topology Tf and functions approximately continuous with respect to f are considered. We prove that (ℝ2, Tf) is a completely regular topological space and we study conditions under which topologies generated by two functions f and g are equal.

scholarly journals A category analogue of the generalization of Lebesgue density topology

2009 ◽  
Vol 42 (1) ◽  
pp. 11-25
Author(s):  
Wojciech Wojdowski
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Density Point ◽  
Density Topology ◽  
The Real ◽  
Lebesgue Density ◽  
Real Anal

Abstract . A notion of AI -topology, a generalization of Wilczy´nski’s I-density topology (see [Wilczy´nski, W.: A generalization of the density topology, Real. Anal. Exchange 8 (1982-1983), 16-20] is introduced. The notion is based on his reformulation of the definition od Lebesgue density point. We consider a category version of the topology, which is a category analogue of the notion of an Ad- -density topology on the real line given in [Wojdowski, W.: A generalization ofdensity topology, Real. Anal. Exchange 32 (2006/2007), 1-10]. We also discuss the properties of continuous functions with respect to the topology.

scholarly journals Ψ-continuous functions and functions preserving ψ-density points

2009 ◽  
Vol 42 (1) ◽  
pp. 175-186
Author(s):  
Małgorzata Filipczak ◽  
Małgorzata Terepeta
Keyword(s):  
Continuous Functions ◽  
Density Topology ◽  
The Family ◽  
Fixed Function

Abstract Let Tψ be the ψ-density topology for a fixed function ψ. We will examine some new properties of the family of ψ-continuous functions (that means continuous functions ƒ: ℝ →ℝ with ψ-density topology Tψ in its domain and range). In the second part of the article we will discuss functions preserving ψ-density points

scholarly journals A new approach to ψ-continuity

2009 ◽  
Vol 42 (1) ◽  
pp. 107-117
Author(s):  
Małgorzata Terepeta
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
New Approach ◽  
Density Topology ◽  
The Family ◽  
Real Anal ◽  
Fixed Function

Abstract Let Tψ be a ψ-density topology for a fixed function ψ. For any topological space X with the topology τ we will consider the family C (X, ℝψ) of all continuous functions f from (X, τ) into (ℝ, Tψ). The main aim of this paper is to investigate when C (X, ℝψ) is a ring. This article is based on the results achieved by M. Knox [A characterization of rings of density continuous functions, Real Anal. Exchange 31 (2005), 165-177].

TEORI KECERDASAN, PENDIDIKAN ANAK, DAN KOMUNIKASI DALAM KELUARGA

1970 ◽  
Vol 6 (1) ◽  
Author(s):  
Muskinul Fuad
Keyword(s):  
Multiple Intelligences ◽  
Educational Activity ◽  
Howard Gardner ◽  
Human Beings ◽  
Brain Functions ◽  
Starting Point ◽  
The Family ◽  
Education Today ◽  
The Brain ◽  
Spatial Logics

The education system in Indonesia emphasize on academic intelligence, whichincludes only two or three aspects, more than on the other aspects of intelligence. For thatreason, many children who are not good at academic intelligence, but have good potentials inother aspects of intelligence, do not develop optimally. They are often considered and labeledas "stupid children" by the existing system. This phenomenon is on the contrary to the theoryof multiple intelligences proposed by Howard Gardner, who argues that intelligence is theability to solve various problems in life and produce products or services that are useful invarious aspects of life.Human intelligence is a combination of various general and specific abilities. Thistheory is different from the concept of IQ (intelligence quotient) that involves only languageskills, mathematical, and spatial logics. According to Gardner, there are nine aspects ofintelligence and its potential indicators to be developed by each child born without a braindefect. What Gardner suggested can be considered as a starting point to a perspective thatevery child has a unique individual intelligence. Parents have to treat and educate theirchildren proportionally and equitably. This treatment will lead to a pattern of education that isfriendly to the brain and to the plurality of children’s potential.More than the above points, the notion that multiple intelligences do not just comefrom the brain needs to be followed. Humans actually have different immaterial (spiritual)aspects that do not refer to brain functions. The belief in spiritual aspects and its potentialsmeans that human beings have various capacities and they differ from physical capacities.This is what needs to be addressed from the perspective of education today. The philosophyand perspective on education of the educators, education stakeholders, and especially parents,are the first major issue to be addressed. With this step, every educational activity andcommunication within the family is expected to develop every aspect of children'sintelligence, especially the spiritual intelligence.

scholarly journals WD40-repeat 47, a microtubule-associated protein, is essential for brain development and autophagy

2017 ◽  
Vol 114 (44) ◽  
pp. E9308-E9317 ◽  
Author(s):  
Meghna Kannan ◽  
Efil Bayam ◽  
Christel Wagner ◽  
Bruno Rinaldi ◽  
Perrine F. Kretz ◽  
...  
Keyword(s):  
Corpus Callosum ◽  
Brain Development ◽  
Brain Connectivity ◽  
Neuronal Morphology ◽  
Dependent Manner ◽  
Wd40 Repeat ◽  
Starting Point ◽  
Neuronal Regulation ◽  
The Family ◽  
Cervical Ganglion

The family of WD40-repeat (WDR) proteins is one of the largest in eukaryotes, but little is known about their function in brain development. Among 26 WDR genes assessed, we found 7 displaying a major impact in neuronal morphology when inactivated in mice. Remarkably, all seven genes showed corpus callosum defects, including thicker (Atg16l1, Coro1c, Dmxl2, and Herc1), thinner (Kif21b and Wdr89), or absent corpus callosum (Wdr47), revealing a common role for WDR genes in brain connectivity. We focused on the poorly studied WDR47 protein sharing structural homology with LIS1, which causes lissencephaly. In a dosage-dependent manner, mice lacking Wdr47 showed lethality, extensive fiber defects, microcephaly, thinner cortices, and sensory motor gating abnormalities. We showed that WDR47 shares functional characteristics with LIS1 and participates in key microtubule-mediated processes, including neural stem cell proliferation, radial migration, and growth cone dynamics. In absence of WDR47, the exhaustion of late cortical progenitors and the consequent decrease of neurogenesis together with the impaired survival of late-born neurons are likely yielding to the worsening of the microcephaly phenotype postnatally. Interestingly, the WDR47-specific C-terminal to LisH (CTLH) domain was associated with functions in autophagy described in mammals. Silencing WDR47 in hypothalamic GT1-7 neuronal cells and yeast models independently recapitulated these findings, showing conserved mechanisms. Finally, our data identified superior cervical ganglion-10 (SCG10) as an interacting partner of WDR47. Taken together, these results provide a starting point for studying the implications of WDR proteins in neuronal regulation of microtubules and autophagy.

scholarly journals Preliminary study of the enzyme ubiquitin carboxylterminal hydrolase 14 (UBP6) in Giardia intestinalis: structural bioinformatic analysis and transcriptional profile during encystation

2015 ◽  
Vol 43 (2) ◽  
pp. 32-40
Author(s):  
Magda E Alvarado ◽  
Camila A González ◽  
Moisés Wasserman ◽  
Claudia C Rubiano
Keyword(s):  
Protein Turnover ◽  
Bioinformatic Analysis ◽  
Giardia Intestinalis ◽  
Deubiquitinating Enzyme ◽  
Combined Approach ◽  
Protein Coding ◽  
Starting Point ◽  
The Family ◽  
Preliminary Study ◽  
Carboxyl Terminal

This paper presents a combined approach<br />with two aims. The first is to analyze the<br />reported sequence of the enzyme ubiquitin<br />carboxyl-terminal hydrolase 14 of Giardia<br />intestinalis (UBP6) through computational<br />methods to find components related with<br />its hypothetical function. The second is<br />to determine if the protein-coding gene is<br />expressed in G. intestinalis and, if such is<br />the case, also determine its transcription<br />pattern along the life cycle of the parasite. It<br />was established that the protein belongs to<br />the family of Cys-dependent deubiquitinases<br />and more specifically to ubiquitin specific<br />proteases (USPs). Moreover, the catalytic<br />center with the complete triad as well as<br />typical features of the USP motif were also<br />identified. Since the computational findings<br />suggest that the enzyme could be functional,<br />reverse transcription coupled to PCR was<br />used as a first approach to establish if in fact<br />the coding gene is expressed in the parasite.<br />Interestingly, it was found not only that<br />the gene is expressed, but also that there<br />is a transcription variation along the life<br />cycle of the parasite. These two findings are<br />the starting point for further studies since<br />they tentatively suggest that this enzyme<br />could be involved in the protein turnover<br />that occurs during parasite encystation.<br />Although preliminary, this study is the first<br />report concerning the study of a specific<br />deubiquitinating enzyme in the parasite G.<br />intestinalis.

scholarly journals Density topology and pointwise convergence

2003 ◽  
Vol 4 (2) ◽  
pp. 509 ◽  
Author(s):  
Wladyslaw Wilczynski
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Density Topology ◽  
Topology Of Pointwise Convergence

<p>We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.</p>

Značaj saradnje školske ustanove i porodice za razvoj ličnosti učenika

2021 ◽  
Author(s):  
Jasmina Veljković ◽  
Keyword(s):  
School Climate ◽  
Relevant Literature ◽  
Living System ◽  
Parenting Skills ◽  
Pedagogical Documentation ◽  
Historical Method ◽  
Starting Point ◽  
The Family ◽  
Changing Patterns ◽  
The Individual

The family as a living system is an organizedand permanent whole with changing patterns of human behavior, ie the family is the first life and social environment in which the child finds himself and acquires the first experiences that form the starting point of the overall development of the individual. In addition to the family, the time that the child spends in school is relatively long, and accordingly, she manages to achieve her influence on the development and formation of the student's personality. The cooperation established between the family and the school can contribute to both parties in different ways, improving the general atmosphere, the school climate and improving the work of teachers and providing support for the development of the family and parenting skills. By studying the relevant literature, we want to determine the importance of cooperation between the family and the school for the development of students' personalities, which is also the basic goal. The paper uses the historical method, as the basic method of historical research and analysis of the content of pedagogical documentation.

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