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An embedding of the Cantor fan into the Lelek fan
Get PDFThe Lelek fan is usually constructed as a subcontinuum of the Cantor fan
in such a way that the set of the end-points of is dense in . It easily
follows that the Lelek fan is embeddable into the Cantor fan. {It is also a
well-known fact that the Cantor fan is embeddable into the Lelek fan, but this
is less obvious. When proving this, one usually uses the well-known result by
Dijkstra and van Mill that the Cantor set is embeddable into the complete
Erd\"os space, and the well-known fact by Kawamura, Oversteegen, and Tymchatyn
that the set of end-points of the Lelek fan is homeomorphic to the complete
Erd\"os space. Then, the subcontinuum of the Lelek fan that is induced by the
embedded Cantor set into the set of end-points of the Lelek fan, is a Cantor
fan.
In our paper, we give an alternative straightforward construction of a Cantor
fan into the Lelek fan. We do not use the fact that the Cantor set is
embeddable into the complete Erd\"os space and that it is homeomorphic to the
set of end-points of the Lelek fan. Instead, we use our recent techniques of
Mahavier products of closed relations to produce an embedding of the Cantor fan
into the Lelek fan. Since the Cantor fan is universal for the family of all
smooth fans, it follows that also the Lelek fan is universal for smooth fans
Lelek maps and n-dimensional maps from compacta to polyhedra
No full textAbstractFor a natural number m⩾0, a map f:X→Y from a compactum X to a metric space Y is an m-dimensional Lelek map if the union of all non-trivial continua contained in the fibers of f is of dimension ⩽m. In [M. Levin, Certain finite-dimensional maps and their application to hyperspaces, Israel J. Math. 105 (1998) 257–262], Levin proved that in the space C(X,I) of all maps of an n-dimensional compactum X to the unit interval I=[0,1], almost all maps are (n−1)-dimensional Lelek maps. Moreover, he showed that in the space C(X,Ik) of all maps of an n-dimensional compactum X to the k-dimensional cube Ik (k⩾1), almost all maps are (n−k)-dimensional Lelek maps. In this paper, we generalize Levin's result. For any (separable) metric space Y, we define the piecewise embedding dimension ped(Y) of Y and we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a complete metric ANR Y, almost all maps are (n−k)-dimensional Lelek maps, where k=ped(Y). As a corollary, we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a Peano curve Y, almost all maps are (n−1)-dimensional Lelek maps and in the space C(X,M) of all maps of an n-dimensional compactum X to a k-dimensional Menger manifold M, almost all maps are (n−k)-dimensional Lelek maps. It is known that k-dimensional Lelek maps are k-dimensional maps for k⩾0
Analysis of key factors of contemporary „financial crisis" and its impacts on development of world economy
Get PDFThe paper deals with key factors of contemporary „financial crisis“ and their impacts on the development of world economy. First of all, the most important factors that caused the crisis are identified and their share on formation of
contemporary negative development trends of financial system is analyzed. Afterwards, their consequences on the development of world economy are assessed both from practical and theoretical points of view. Pursued analysis is focused on two basic spheres. First of all, it deals with negative economic factors that are explored from the point of view of all sorts of economic
subjects – it means households, companies and states. And what is especially important, it is focused on man himself (or herself) as he or she has “primary” influence on the development of world economy and thus the whole human society.
Finally, the matter of effectiveness of up-to now used anti-crisis measures are discussed, where possible negative impacts that can be caused by their long-term use are assessed. Last of all, possibility of global financial crisis that might cause collapse of world economy is outlined
USER GENERATED CONTENT DI MEDIA SOSIAL TIKTOK SEBAGAI STRATEGI PROMOSI BISNIS LELEK AUTO LIGHT
Get PDFThe aim of this research is to find out business promotion strategies using user generated content in a car light custom repair shop, namely Lelek Auto Light. In the research, the concept used is user generated content and also the strategy stages which are carried out through the strategy stage concept. The research method used is descriptive qualitative with interview, observation and documentation data collection methods. The results of this research are that Lelek Auto Light uses 3 promotional strategy stages, namely the planning, implementation and evaluation stages. At the planning stage, problem analysis, audience analysis, formulating communication objectives, determining media channels and planning media production are used. In the implementation stage, namely utilizing TikTok social media and managing user generated content which is done with Lelek Auto Light, producing video content to be used as a reference by users. At the evaluation stage, strategy evaluation is carried out and also evaluation of the results of the strategies that have been used
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Zero span continua
No full textThis dissertation is concerned with the span of continua and with continua in class W. The emphasis of this study is on the class of continua which have zero span. The relationship between this class and class W is studied. The author introduces in this dissertation the notion of the symmetric span of a continuum by modifying Lelek's origional definition. Continua with zero span have zero symmetric span but the converse does not hold. The author proves that the continua with zero symmetric span are in class W. Lelek defined the semispan of a continuum M by relaxing a condition in the definition of span. Lelek gives an example of a continuum for which the span and semispan are different. The author shows that if every subcontinuum of the continuum M is in class W, then the span and semispan of M are the same. This result and the previous one are then applied to show that the span of a continuum is zero if and only if the semispan is zero. This has the corollary that continua with zero span have the fixed point property. A second corollary of this theorem generalizes a recent result of Duda and Kell to the following: If H and K are continua with zero span which intersect, H n K is connected, and H u K is atriodic then H u K has zero span. Next, decomposable, atriodic continua are studied. After preliminary lemmas. It is shown that if H and K are continua in class W which intersect, H n K is connected, and H u K is atriodic then H u K is in class W. Finally certain homogeneous continua are studied. It is shown that homogeneous, almost chainable continua have zero span.Mathematics, Department o
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The space of Lelek fans in the Cantor fan is homeomorphic to Hilbert space
No full textWe show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous. © 2010 The Mathematical Society of Japan
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