CARDINALITY OF INVERSE LIMITS WITH UPPER SEMICONTINUOUS BONDING FUNCTIONS

2014 ◽  
Vol 91 (1) ◽  
pp. 167-174 ◽  
Author(s):  
MATEJ ROŠKARIČ ◽  
NIKO TRATNIK
Keyword(s):  
Recent Result ◽  
Inverse Limit ◽  
Inverse Limits ◽  
Semicontinuous Function ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Function

AbstractWe explore the cardinality of generalised inverse limits. Among other things, we show that, for any $n\in \{ℵ_{0},c,1,2,3,\dots \}$, there is an upper semicontinuous function with the inverse limit having exactly $n$ points. We also prove that if $f$ is an upper semicontinuous function whose graph is a continuum, then the cardinality of the corresponding inverse limit is either 1, $ℵ_{0}$ or $c$. This generalises the recent result of I. Banič and J. Kennedy, which claims that the same is true in the case where the graph is an arc.

scholarly journals PAIRS OF HAHN AND SEPARATELY CONTINUOUS FUNCTION

2021 ◽  
Vol 9 (1) ◽  
pp. 210-229
Author(s):  
O. Maslyuchenko ◽  
A. Kushnir
Keyword(s):  
Continuous Function ◽  
Lower Semicontinuous ◽  
Lower Semicontinuous Function ◽  
Normal Space ◽  
Semicontinuous Function ◽  
Upper Semicontinuous ◽  
Pseudocompact Space ◽  
Upper Semicontinuous Function ◽  
Perfectly Normal Space ◽  
Perfectly Normal

In this paper we continue the study of interconnections between separately continuous function which was started by V. K. Maslyuchenko. A pair (g, h) of functions on a topological space is called a pair of Hahn if g ≤ h, g is an upper semicontinuous function and h is a lower semicontinuous function. We say that a pair of Hahn (g, h) is generated by a function f, which depends on two variables, if the infimum of f and the supremum of f with respect to the second variable equals g and h respectively. We prove that for any perfectly normal space X and non-pseudocompact space Y every pair of Hahn on X is generated by a continuous function on X x Y . We also obtain that for any perfectly normal space X and for any space Y having non-scattered compactification any pair of Hahn on X is generated by a separately continuous function on X x Y .

scholarly journals Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory

2012 ◽  
Vol 111 (2) ◽  
pp. 296
Author(s):  
Benedikt Steinar Magnússon
Keyword(s):  
Complex Manifold ◽  
Plurisubharmonic Function ◽  
Local Theory ◽  
Semicontinuous Function ◽  
Plurisubharmonic Functions ◽  
The Real ◽  
Upper Semicontinuous ◽  
The Difference ◽  
Upper Semicontinuous Function

We generalize the Poletsky disc envelope formula for the function $\sup \{u\in \mathcal{PSH}(X,\omega); u\leq \phi\}$ on any complex manifold $X$ to the case where the real $(1,1)$-current $\omega=\omega_1-\omega_2$ is the difference of two positive closed $(1,1)$-currents and $\varphi$ is the difference of an $\omega_1$-upper semicontinuous function and a plurisubharmonic function.

scholarly journals Riesz's Functions in Weighted Hardy and Bergman Spaces

1996 ◽  
Vol 48 (5) ◽  
pp. 930-945 ◽  
Author(s):  
Takahiko Nakazi ◽  
Masahiro Yamada
Keyword(s):  
Hardy Spaces ◽  
Borel Measure ◽  
Bergman Spaces ◽  
Semicontinuous Function ◽  
Positive Borel Measure ◽  
Upper Semicontinuous ◽  
Hardy And Bergman Spaces ◽  
Upper Semicontinuous Function ◽  
Image Position ◽  
Bergman And Hardy Spaces

AbstractLet μ be a finite positive Borel measure on the closed unit disc . For each a in , put where ƒ ranges over all analytic polynomials with f(a) = 1. This upper semicontinuous function S(a) is called a Riesz's function and studied in detail. Moreover several applications are given to weighted Bergman and Hardy spaces.

scholarly journals Lp-GENERIC COCYCLES HAVE ONE-POINT LYAPUNOV SPECTRUM

2003 ◽  
Vol 03 (01) ◽  
pp. 73-81 ◽  
Author(s):  
ALEXANDER ARBIETO ◽  
JAIRO BOCHI
Keyword(s):  
Lyapunov Exponents ◽  
Lyapunov Spectrum ◽  
Semicontinuous Function ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Function

We show that the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the Lp topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the Lp-generic cocycle, p < ∞, are all equal.

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals Super-extremal processes and the argmax process

1994 ◽  
Vol 31 (04) ◽  
pp. 958-978 ◽  
Author(s):  
Sidney I. Resnick ◽  
Rishin Roy
Keyword(s):  
Metric Space ◽  
Semicontinuous Function ◽  
Closed Set ◽  
Continuous Choice ◽  
Extremal Processes ◽  
Upper Semicontinuous Function ◽  
Classical Vector ◽  
Vector Valued ◽  
Path Properties ◽  
Separable Metric Space

In this paper, we develop the probabilistic foundations of the dynamic continuous choice problem. The underlying choice set is a compact metric space E such as the unit interval or the unit square. At each time point t, utilities for alternatives are given by a random function . To achieve a model of dynamic continuous choice, the theory of classical vector-valued extremal processes is extended to super-extremal processes Y = {Yt, t &gt; 0}. At any t &gt; 0, Y t is a random upper semicontinuous function on a locally compact, separable, metric space E. General path properties of Y are discussed and it is shown that Y is Markov with state-space US(E). For each t &gt; 0, Y t is associated. For a compact metric E, we consider the argmax process M = {Mt, t &gt; 0}, where . In the dynamic continuous choice application, the argmax process M represents the evolution of the set of random utility maximizing alternatives. M is a closed set-valued random process, and its path properties are investigated.

On inverse limits of monounary algebras

2014 ◽  
Vol 64 (3) ◽  
Author(s):  
Emília Halušková
Keyword(s):  
Inverse Limit ◽  
Inverse Limits

AbstractWe study inverse limits of monounary algebras. All monounary algebras A such that A can arise from A only by an inverse limit construction are described. We deal with an existence of an inverse limit. Some inverse limit closed classes are described. The paper ends with two problems.

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