Related papers: The principle of pointfree continuity
In this research article, we discuss two topics. Firstly, we introduce SCC-Map and $\phi$-contraction type $T$-coupling. By using these two definitions, we generalize $\phi$-contraction type coupling given by H. Aydi et al. [3] to…
We establish the existence of the universal type structure in presence of conditioning events without any topological assumption, namely, a type structure that is terminal, belief-complete, and non-redundant, by performing a construction…
Topology change is considered to be a necessary feature of quantum gravity by some authors, and impossible by others. One of the main arguments against it is that spacetimes with changing spatial topology have bad causal properties. Borde…
Concept of bi-soft topological spaces is introduced. Several notions of a soft topological space are generalized to study bi-soft topological spaces. Separation axioms play a vital role in study of topological spaces. These concepts have…
We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse…
The Omitting Types Theorem in model theory and the Baire Category Theorem in topology are known to be closely linked. We examine the precise relation between these two theorems. Working with a general notion of logic we show that the…
We study conditional independence under infinite measures on punctured product spaces, a notion recently introduced for graphical modeling in multivariate extremes and L\'evy processes. In contrast to classical probabilistic conditional…
Cubical type theories are designed around an abstract unit interval from which types of paths, used to represent equalities, are defined. Varying the operations available on this interval yields different type theories. A reversal is an…
In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…
We provide a complete characterization of periodic point free homeomorphisms of the $2$-torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$-torus without periodic points and exhibiting…
Suppose that E is a Banach space, {\tau} a topology under which the norm of E becomes {\tau}-lower semicontinuous and S a commuting family of {\tau}-continuous nonexpansive mappings defined on a {\tau}-compact convex subset C of E: It is…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We examine topological spaces not distinguishing ideal pointwise and ideal $\sigma$-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal…
Extending Mart\'in Escard\'o's effectful forcing technique, we give a new proof of a well-known result: Brouwer's monotone bar theorem holds for any bar that can be realized by a functional of type $(\mathbb{N} \to \mathbb{N}) \to…
In intuitionistic mathematics, the Brouwer Continuity Theorem states that all total real functions are (uniformly) continuous on the unit interval. We study this theorem and related principles from the point of view of Reverse Mathematics…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
The existence of least finite support is used throughout the subject of nominal sets. In this paper we give some Brouwerian counterexamples showing that constructively, least finite support does not always exist and in fact can be quite…
Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^2$ and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f…