相关论文: How a Change to Topology's Union Axiom Affects Con…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact if and only if every sequence has a…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e., an open subset homeomorphic to an open interval). A special attention is paid to relationships between topological transitivity, weak and…
Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
We present some sufficient conditions for continuity of the mapping $f:\langle X,\tau_X^*\rangle \to \langle Y,\tau_Y^*\rangle$, where $\tau_X^*$ and $\tau_Y^*$ are topologies induced by the local function on $X$ and $Y$, resp. under the…
Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving…
We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown…
This paper introduces a novel topology, referred to as the star topology, on finite graphs. By treating vertices and edges as points in a unified space, we explore continuous maps between Bare representations of a graph and their…
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…
A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…
Exact string solutions are presented, providing backgrounds where a dynamical change of topology is occuring. This is induced by the time variation of a modulus field. Some lessons are drawn concerning the region of validity of effective…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…