On upper and lower contra-ω-continuous multifunctions
... Various types of functions play a significant role in the theory of classical point set topology. A great number of papers dealing with such functions have appeared, and a good many of them have been extended to the setting of multifunction [13],[3],[4],[5],[6]. A. Al-Omari et. al. introduced the co ...
... Various types of functions play a significant role in the theory of classical point set topology. A great number of papers dealing with such functions have appeared, and a good many of them have been extended to the setting of multifunction [13],[3],[4],[5],[6]. A. Al-Omari et. al. introduced the co ...
AN INTRODUCTION TO HYPERLINEAR AND SOFIC GROUPS 1
... In these lectures, we will deal with a class of groups called hyperlinear groups, as well as its (possibly proper) subclass, that of sofic groups. One natural way to get into this line of research is through the theory of operator algebras. Here, the hyperlinear groups are sometimes referred to as “ ...
... In these lectures, we will deal with a class of groups called hyperlinear groups, as well as its (possibly proper) subclass, that of sofic groups. One natural way to get into this line of research is through the theory of operator algebras. Here, the hyperlinear groups are sometimes referred to as “ ...
INTEGRABILITY CRITERION FOR ABELIAN EXTENSIONS OF LIE
... sequentially complete locally convex topological vector spaces. These spaces have the property that every continuous path has a Riemann integral. We adopt the following notion of smoothness. Definition 2.1. Let E, F be sequentially complete locally convex topological vector spaces over R (or C) and ...
... sequentially complete locally convex topological vector spaces. These spaces have the property that every continuous path has a Riemann integral. We adopt the following notion of smoothness. Definition 2.1. Let E, F be sequentially complete locally convex topological vector spaces over R (or C) and ...
Topological spaces
... Every metric space (X, d) comes equipped with a natural choice of topology Td , called the metric topology, defined by Td = {U ⊂ X | ∀p ∈ U ∃r > 0 such that Bp (r) ⊂ U } The reader will, no doubt, have noticed that this definition agrees with the definition of the Euclidean topology from example 2.1 ...
... Every metric space (X, d) comes equipped with a natural choice of topology Td , called the metric topology, defined by Td = {U ⊂ X | ∀p ∈ U ∃r > 0 such that Bp (r) ⊂ U } The reader will, no doubt, have noticed that this definition agrees with the definition of the Euclidean topology from example 2.1 ...
