General Topology-I

  title={General Topology-I},
  author={Nitakshi Goyal},
  • N. Goyal
  • Published 16 December 2017
  • Mathematics
On the 𝑯-space and the product of two 𝑯-spaces
Considering the set of real numbers R, for each x ∈ A, B(x)={(x−ϵ,x+ϵ):ϵ>0}, and for each x∈ R\A, let B(x)={[x,x+ϵ):ϵ>0}, the unique topology generated by {B(x): x ∈ R} is denoted by τ(A) and ( R ,
Computing with continuous objects: a uniform co-inductive approach
  • D. Spreen
  • Mathematics
    Mathematical Structures in Computer Science
  • 2021
A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets, and uniformly continuous maps is presented and is of the same computational power as Weihrauch's Type-Two Theory of Effectivity.
Completeness in quasi-pseudometric spaces
The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric
Similarity Structure and Emergent Properties
The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as
Convex Optimization Techniques for Geometric Covering Problems
The present thesis is a commencement of a generalization of covering results in specific settings, such as the Euclidean space or the sphere, to arbitrary compact metric spaces, and relies in part on the moment methods developed by de Laat and Vallentin for the packing problem on topological packing graphs.
Product of generalized quasi-uniform spaces
In this paper, we introduce product \(g\)-quasi uniformity and show that product \(g\)-quasi uniformity induces the generalized product topology. We also provide a necessary and sucient condition for
On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers
In this paper we study submonoids of the monoid $\mathscr{I}_{\infty}^{\,\Rsh\!\!\nearrow}(\mathbb{N})$ of almost monotone injective co-finite partial selfmaps of positive integers $\mathbb{N}$. Let
On closed mappings of 𝜎-compact spaces and dimension
  • E. Pol, R. Pol
  • Computer Science
    Proceedings of the American Mathematical Society
  • 2019
A remainder of the Hilbert space, a metrizable compact extension of theinline-formula content-type="math/mathml", where the inline- formula is a space homeomorphic to the X-tex space.
A topological space X is called C-regular if there exists a oneto-one function f from X onto a regular space Y such that the restriction f|K : K −→ f(K) is a homeomorphism for each compact subspace K
Similarity Structure on Scientific Theories
I review and amplify on some of the many uses of representing a scientific theory in a particular context as a collection of models endowed with a similarity structure, which encodes the ways in