Related papers: Soft $T_{(0,\alpha)}$ Spaces
A topological space $X$ is defined to have an $\omega^\omega$-base if at each point $x\in X$ the space $X$ has a neighborhood base $(U_\alpha[x])_{\alpha\in\omega^\omega}$ such that $U_\beta[x]\subset U_\alpha[x]$ for all $\alpha\le\beta$…
The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…
We study the topology of the complex points of the algebraic loop space of a smooth curve.
Let $\kappa$ be an infinite regular cardinal. We define a topological space $X$ to be $T_{\kappa-Borel}$-space (resp. a $T_{\kappa-BP}$-space) if for every $x\in X$ the singleton $\{x\}$ belongs to the smallest $\kappa$-additive algebra of…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
Soft materials consist of basic units that are significantly larger than an atom but much smaller than the overall dimensions of the sample. The label "soft condensed matter" emphasizes that the large basic building blocks of these…
We show how recent exact results in supersymmetric theories can be extended to models which include {\it explicit} soft supersymmetry breaking terms. We thus derive new exact results for non-supersymmetric models.
We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…
A ten-dimensional supersymmetric $E_8$ gauge theory is compactified over six-dimensional coset spaces, establishing further our earlier conjecture that the resulting four dimensional theory is a softly broken supersymmetric gauge theory in…
The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…
In this paper we determine extensions of higher degree between indecomposable modules over gentle algebras. In particular, our results show how such extensions either eventually vanish or become periodic. We give a geometric interpretation…
We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…
A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…
Let X be a smooth projective surface over a number field, and $f: X \to X$ an automorphism of positive topological entropy. In this paper, we construct a height function on X that behaves well relative to f and deduce some arithmetic…
Orbifold compactifications with continuous Wilson lines have very interesting characteristics and as a consequence they are candidates to obtain realistic models. We perform an analysis of the soft supersymmetry-breaking terms arising in…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
Let $A$ be a real soft function algebra. In arXiv:2208.11431 we have obtained a canonical splitting $\mathrm{H}^* (\Omega ^\bullet _{A|\mathrm{R}}) \cong \mathrm{H} ^* (X,\mathrm{R})\oplus \text{(something)}$ via the canonical maps…
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We…
Soft theorems in gauge theory and gravity encode the universal properties of scattering amplitudes as the zero frequency limit of one or more external states is approached. When the participating particles are treated in the massless limit,…