Related papers: On proper and exterior sequentiality
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
In [8] the authors initiate the study of selective versions of the notion of $\theta$-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising…
The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
Leveraging topos theory a semantics can be given to sequential circuits where time-sensitive gates, such as unit delay, are treated uniformly with combinational gates. Both kinds of gates are functions in a particular topos: the topos of…
In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.
The arising of central extensions is discussed in two contexts. At first classical counterparts of quantum anomalies (deserving being named as "classical anomalies") are associated with a peculiar subclass of the non-equivariant maps.…
The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the…
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
Based on the Carath\'eodory -Pesin structure theory[11], we introduce three notions of topological pressure of a proper map and provide some properties of these notions. For the proper map of a locally compact separable metric space, we…
Moving beyond the dualistic view in AI where agent and environment are separated incurs new challenges for decision making, as calculation of expected utility is no longer straightforward. The non-dualistic decision theory literature is…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…
We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spaces, respectively. An order topology is introduced such that…
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…