390 - kfupm
... called weakly BR-continuity. In this paper we define the notion of weakly BR-openness as a natural dual to the weakly BR continuity by using the notion of b-θ-open and b-θ-closed sets. We obtain several characterizations and properties of these functions. Moreover, we also study these functions comp ...
... called weakly BR-continuity. In this paper we define the notion of weakly BR-openness as a natural dual to the weakly BR continuity by using the notion of b-θ-open and b-θ-closed sets. We obtain several characterizations and properties of these functions. Moreover, we also study these functions comp ...
The No Retraction Theorem and a Generalization
... Armed with the appropriate generalization of a boundary on 2-dimensional simplicial complexes, we are equipped to provide the corresponding generalization of the No-Retraction Theorem. First, however, we require a simple lemma from graph theory. Lemma 1. Let G be a graph with no loops, that is, no e ...
... Armed with the appropriate generalization of a boundary on 2-dimensional simplicial complexes, we are equipped to provide the corresponding generalization of the No-Retraction Theorem. First, however, we require a simple lemma from graph theory. Lemma 1. Let G be a graph with no loops, that is, no e ...
Some Types Of Compactness Via Ideal
... by τ(x) = {U∈τ : x∈U}. Let (X, τ, I) be a topological space with ideal I and A⊆X, then the local function of A with respect to I and τ [14] A*(I)= {x∈X:U∩A∉I for each U∈τ (x)}. For every topological space (X,τ,I) with ideal I, there exists a topology τ*(I), finer than τ , generated by the base (I,τ ...
... by τ(x) = {U∈τ : x∈U}. Let (X, τ, I) be a topological space with ideal I and A⊆X, then the local function of A with respect to I and τ [14] A*(I)= {x∈X:U∩A∉I for each U∈τ (x)}. For every topological space (X,τ,I) with ideal I, there exists a topology τ*(I), finer than τ , generated by the base (I,τ ...
Math 396. Quotients by group actions Many important manifolds are
... G = Q on R via additive translations (with Q given the discrete topology, so as to fit into the above framework). This is a continuous action, but the quotient R/Q is very bad: any two Q-orbits in R contain arbitrarily close points! However, there are more subtle examples where things go wrong: Exam ...
... G = Q on R via additive translations (with Q given the discrete topology, so as to fit into the above framework). This is a continuous action, but the quotient R/Q is very bad: any two Q-orbits in R contain arbitrarily close points! However, there are more subtle examples where things go wrong: Exam ...
Some facts from descriptive set theory concerning essential spectra
... semigroups exhibit a nice behavior. In particular, we establish that the infinitesimal generator of any strongly continuous group is necessarily bounded (which seems to be a feature of this class of spaces). 2. Preliminaries. In this section we will collect some notions and tools from functional ana ...
... semigroups exhibit a nice behavior. In particular, we establish that the infinitesimal generator of any strongly continuous group is necessarily bounded (which seems to be a feature of this class of spaces). 2. Preliminaries. In this section we will collect some notions and tools from functional ana ...