Related papers: Connected Generalized Inverse Limits and Intermedi…
In this paper, we consider inverse limits of [0,1] using upper semicontinuous set-valued bonding functions with the intermediate value property. Expanding on classical results by Barge and Martin, we explore the relationship between…
Although inverse limits with factor spaces indexed by the positive integers are most commonly studied, Ingram and Mahavier have defined inverse limits with set-valued functions broadly enough for any directed index set to be used. In this…
In this paper, we consider inverse limits of $[0,1]$ using upper semicontinuous set-valued functions. We aim to expand on a previous paper exploring the relationship between the existence periodic points of a continuous function to the…
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…
In this paper, we show that a uniform hypergraph $\mathcal{G}$ is connected if and only if one of its inverse Perron values is larger than $0$. We give some bounds on the bipartition width, isoperimetric number and eccentricities of…
We show that two inverse limits of inverse sequences of closed intervals and quasi Markov bonding functions are homeomorphic, if the inverse sequences follow the same pattern. This significantly improves Holte's result about when two…
Clearly, a generalized inverse limit of metrizable spaces indexed by $\mathbb N$ is metrizable, as it is a subspace of a countable product of metrizable spaces. The authors previously showed that all idempotent, upper semi-continuous,…
It is proved that the exchange property, the Bass stable rank and the quasi-Bass property are all preserved under surjective inverse limits. This is then applied to multiplier rings by showing that in many cases can be obtained as inverse…
We introduce countably Markov interval functions and show that two inverse limits with countably Markov interval bonding functions are homeomorphic if the functions follow the same pattern. This result presents a generalization of…
In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…
Let $\ell_j:=-\frac{d^2}{dx^2}+k^2q_j(x),$ $k=const>0, j=1,2,$ $0<c_0\leq q_j(x)\leq c_1,$ %$q\in BV([0,1])$, $q$ has finitely many discontinuity points $x_m\in [0,1],$ and is real-analytic on the intervals $[x_m,x_{m+1}]$ between these…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…
We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets…
During the study of the topic of limit summability of functions (introduced by the author in 2001), we encountered some types of functions that are related to the mean value theorem. In this paper, we formally define mean value and…