Related papers: Bi-topological spaces and the Continuity Problem
We investigate the topological entropy of operators. More precisely, in the Banach space setting, we show that compact operators have finite entropy, which depends solely on their point spectrum. Moreover, for operators on \(F\)-spaces, we…
We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition…
We introduce q-frequently hypercyclic operators and derive a sufficient criterion for a continuous operator to be q-frequently hypercyclic on a locally convex space. Applications are given to obtain q-frequently hypercyclic operators with…
In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…
The prime objective of this paper is to develop the notion of absolute continuity of functions on a more general setting outside $\R$. For this we have considered a topological space which is a measure space as well. We have built axioms…
This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…
The local equicontinuity of an operator $T:X\rightrightarrows X^{*}$ with proper Fitzpatrick function $\varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of…
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…
A function $f$ on a topological space is sequentially continuous at a point $u$ if, given a sequence $(x_{n})$, $\lim x_{n}=u$ implies that $\lim f(x_{n})=f(u)$. This definition was modified by Connor and Grosse-Erdmann for real functions…
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to…
It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics.…
A function f is continuous iff the PRE-image f^{-1}[V] of any open set V is open again. Dual to this topological property, f is called OPEN iff the IMAGE f[U] of any open set U is open again. Several classical Open Mapping Theorems in…
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…
We introduce the effectual topological complexity (ETC) of a $G$-space $X$. This is a $G$-equivariant homotopy invariant sitting in between the effective topological complexity of the pair $(X,G)$ and the (regular) topological complexity of…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
We revisit the results of Kitson and Timoney \emph{[J.~Math.~Anal.~Appl.~\textbf{378} (2011), 680--686]} on the spaceability of complements of operator ranges, extending one of their main theorems to the general Fr\'echet setting. In…
We study expansions of Hilbert spaces with a bounded normal operator $T$. We axiomatize this theory in a natural language and identify all of its completions. We prove the definability of the adjoint $T^*$ and prove quantifier elimination…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be $p_\tau$-bounded…