this PDF file - European Journal of Pure and Applied
... Definition 3 (8). Let (X,τ ) be a topological spaces and µ be a supra topolgy on X. We call µ a supra topology associated with τ if τ ⊂ µ. Definition 4 (8). Let (X,µ) be a supra topological space. A set A is called a supra b-open set if A ⊆ clµ (intµ (A)) ∪ intµ (clµ (A)). The complement of a supra ...
... Definition 3 (8). Let (X,τ ) be a topological spaces and µ be a supra topolgy on X. We call µ a supra topology associated with τ if τ ⊂ µ. Definition 4 (8). Let (X,µ) be a supra topological space. A set A is called a supra b-open set if A ⊆ clµ (intµ (A)) ∪ intµ (clµ (A)). The complement of a supra ...
Applications of some strong set-theoretic axioms to locally compact
... its boundary is H \ H. Let C = D \ D. Then C is closed in X because D is discrete, and C is disjoint from H because H \ H is closed. Hence H is a subset of W = H \ C. Also, D is closed in the relative topology of W . Using the fact that W is strongly cwH, let {Ud : d ∈ D} be a discrete-in-W open exp ...
... its boundary is H \ H. Let C = D \ D. Then C is closed in X because D is discrete, and C is disjoint from H because H \ H is closed. Hence H is a subset of W = H \ C. Also, D is closed in the relative topology of W . Using the fact that W is strongly cwH, let {Ud : d ∈ D} be a discrete-in-W open exp ...
a note on weakly separable spaces
... 4. On weakly separable spaces and some functorial constructions We are going to recall some notions and facts concerning hyperspaces and related spaces. For a topological space X, by exp X one denotes the set of all non-empty closed subsets of X. Let U1 , . . . , Uk be a finite family of open subsets ...
... 4. On weakly separable spaces and some functorial constructions We are going to recall some notions and facts concerning hyperspaces and related spaces. For a topological space X, by exp X one denotes the set of all non-empty closed subsets of X. Let U1 , . . . , Uk be a finite family of open subsets ...
THEORY OF FREDHOLM OPERATORS AND
... for every compact space X. (0.6) is the common generalization of (0.3) and (0.5). Finally a proof of the periodicity theorem of Km -theory is given. This theorem is due to Atiyah and Singer. It does not seem to be easy to translate all known proofs of the periodicity theorem of K-theory to K^ -theor ...
... for every compact space X. (0.6) is the common generalization of (0.3) and (0.5). Finally a proof of the periodicity theorem of Km -theory is given. This theorem is due to Atiyah and Singer. It does not seem to be easy to translate all known proofs of the periodicity theorem of K-theory to K^ -theor ...
1 Introduction
... Proof. Proceeding like the proof of Theorem 1, we see that if there exists a τ -open set U such that A ∪ B ⊂ U , then U = X or U = A ∪ B. If U = A ∪ B 6= X, then A ∪ B is proper τ -open and so by maximal (τ, µ)-openness of A on X, we get A = A ∪ B which implies A is τ -open and B ⊂ A. Since B is max ...
... Proof. Proceeding like the proof of Theorem 1, we see that if there exists a τ -open set U such that A ∪ B ⊂ U , then U = X or U = A ∪ B. If U = A ∪ B 6= X, then A ∪ B is proper τ -open and so by maximal (τ, µ)-openness of A on X, we get A = A ∪ B which implies A is τ -open and B ⊂ A. Since B is max ...
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... Properties of perfectly continuous functions are further elaborated in [11]. The class of perfectly continuous functions properly contains the class of strongly continuous functions of Levine [13] and is strictly contained in the class of cl-supercontinuous (≡clopen continuous) functions introduced ...
... Properties of perfectly continuous functions are further elaborated in [11]. The class of perfectly continuous functions properly contains the class of strongly continuous functions of Levine [13] and is strictly contained in the class of cl-supercontinuous (≡clopen continuous) functions introduced ...
characterizations of feebly totally open functions
... if every two distinct points of X can be separated by disjoint semi-open (resp. clopen) sets. 5. s-normal [34] (resp. ultra-normal [33 & 45]) if each pair of non-empty disjoint closed sets can be separated by disjoint semi-open (resp. clopen) sets. 6. s-regular [26] (resp. ultra regular [33]) if for ...
... if every two distinct points of X can be separated by disjoint semi-open (resp. clopen) sets. 5. s-normal [34] (resp. ultra-normal [33 & 45]) if each pair of non-empty disjoint closed sets can be separated by disjoint semi-open (resp. clopen) sets. 6. s-regular [26] (resp. ultra regular [33]) if for ...
Orbifolds and their cohomology.
... Example 1.0.5. Let G be a finite group. Then one can form an orbifold BG := [•/G] by allowing G to act trivially on a point. In terms of groupoids, this is the category with one object and morphisms given by G. Example 1.0.6. In the definition of weighted projective space given in Example 1.0.3, all ...
... Example 1.0.5. Let G be a finite group. Then one can form an orbifold BG := [•/G] by allowing G to act trivially on a point. In terms of groupoids, this is the category with one object and morphisms given by G. Example 1.0.6. In the definition of weighted projective space given in Example 1.0.3, all ...
