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A CLOSURE PROPERTY FOR THE SOUSLIN OPERATION
... ( X , MEASµ ) admits covers. To see this, for every set D ⊆ X , let D̂ ⊇ D be a Borel set realising the outer measure. Then clearly any measurable subset of D̂ \ D is a null set, whence all its subsets belong to MEASµ . Theorem 4 (E. Szpilrajn-Marczewski). Let ( X , S ) be a measurable space admitti ...
... ( X , MEASµ ) admits covers. To see this, for every set D ⊆ X , let D̂ ⊇ D be a Borel set realising the outer measure. Then clearly any measurable subset of D̂ \ D is a null set, whence all its subsets belong to MEASµ . Theorem 4 (E. Szpilrajn-Marczewski). Let ( X , S ) be a measurable space admitti ...
tychonoff`s theorem - American Mathematical Society
... For completeness, we provide definitions of products and the product topology. Let {Xa\a e J} be a collection of sets. The product Ha€J Xa is defined to be the collection of all functions f: J -* [JaeJ ^° sucn tnat f(°^ e %a ■ We often write / = (xa)a€j or simply (xa) where f(a) = xa . For each a th ...
... For completeness, we provide definitions of products and the product topology. Let {Xa\a e J} be a collection of sets. The product Ha€J Xa is defined to be the collection of all functions f: J -* [JaeJ ^° sucn tnat f(°^ e %a ■ We often write / = (xa)a€j or simply (xa) where f(a) = xa . For each a th ...
IOSR Journal of Mathematics (IOSR-JM)
... O.Njastad, On some classes of nearly open sets, Pacific J.Math.,15(1965),961-970 A.S. Mashhour , I.N.Hasanein and S.N. El-Deeb,α-continuous and α-open mappings, Acta Math.Hungar.,41(1983),213-218. R.Vaidynathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci. Math.Sci., 20(1945) ...
... O.Njastad, On some classes of nearly open sets, Pacific J.Math.,15(1965),961-970 A.S. Mashhour , I.N.Hasanein and S.N. El-Deeb,α-continuous and α-open mappings, Acta Math.Hungar.,41(1983),213-218. R.Vaidynathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci. Math.Sci., 20(1945) ...
219 PROPERTIES OF (γ,γ )-SEMIOPEN SETS C. Carpintero N
... Theorem 4.9 A set E in a topological space X is (γ, γ 0 )-semi-θ-connected if and only if any two points of E are contained in some (γ, γ 0 )-semi-θ-connected set contained in E. Theorem 4.10 The union of any collection of (γ, γ 0 )-semi-θ-connected sets, no two of which are (γ, γ 0 )-semi-θ-separat ...
... Theorem 4.9 A set E in a topological space X is (γ, γ 0 )-semi-θ-connected if and only if any two points of E are contained in some (γ, γ 0 )-semi-θ-connected set contained in E. Theorem 4.10 The union of any collection of (γ, γ 0 )-semi-θ-connected sets, no two of which are (γ, γ 0 )-semi-θ-separat ...