Global Calculus:Basic Motivations
... 3.2. Germs, stalks and etale spaces. Let’s look at two topological spaces X and Y , and a point x in X that we are interested in. We would like those properties of a function that depend only on its value quite close to x. Thus, two functions that coincide in a sufficiently small neighbourhood of th ...
... 3.2. Germs, stalks and etale spaces. Let’s look at two topological spaces X and Y , and a point x in X that we are interested in. We would like those properties of a function that depend only on its value quite close to x. Thus, two functions that coincide in a sufficiently small neighbourhood of th ...
On Submaximality in Intuitionistic
... Some examples of complementary topological invariants are; T1 and “all proper closed sets are finite” ;Door and “filter-connected”;TD and nested; Disconnected and principal of order two (Cameron, 1997; Larson, 1973; Kennedy&Cartan, 1996) The main purpose of this article is to identify those members ...
... Some examples of complementary topological invariants are; T1 and “all proper closed sets are finite” ;Door and “filter-connected”;TD and nested; Disconnected and principal of order two (Cameron, 1997; Larson, 1973; Kennedy&Cartan, 1996) The main purpose of this article is to identify those members ...
Extending Baire–one functions on topological spaces ⋆
... Baire–one function defined on the set of extreme points of a compact convex set to an affine Baire–one function on the whole set). Some problems in this area remained open and it turns out to be worthwhile to better understand the situation in general topological spaces. It is well–known that a Bai ...
... Baire–one function defined on the set of extreme points of a compact convex set to an affine Baire–one function on the whole set). Some problems in this area remained open and it turns out to be worthwhile to better understand the situation in general topological spaces. It is well–known that a Bai ...
On weakly πg-closed sets in topological spaces
... Theorem 3.12 A set A is wπg-closed if and only if cl(int(A)) − A contains no non-empty π- closed set. Proof. Necessity. Let F be a π-closed set such that F ⊆ cl(int(A)) − A. Since F c is π- open and A ⊆ F c , from the definition of wπg-closed set it follows that cl(int(A)) ⊆ F c . ie. F ⊆ (cl(int(A) ...
... Theorem 3.12 A set A is wπg-closed if and only if cl(int(A)) − A contains no non-empty π- closed set. Proof. Necessity. Let F be a π-closed set such that F ⊆ cl(int(A)) − A. Since F c is π- open and A ⊆ F c , from the definition of wπg-closed set it follows that cl(int(A)) ⊆ F c . ie. F ⊆ (cl(int(A) ...
INTRODUCTION TO TOPOLOGY Contents 1. Basic concepts 1 2
... Exercise 1.23. Show that every function from a discrete topological space is continuous. Analogously, verify that every function to a trivial topological space is continuous. Interestingly enough, our definition of continuity is ’global’ in the sense that no reference is made to individual points of ...
... Exercise 1.23. Show that every function from a discrete topological space is continuous. Analogously, verify that every function to a trivial topological space is continuous. Interestingly enough, our definition of continuity is ’global’ in the sense that no reference is made to individual points of ...