The Baire category theorem in products of linear spaces and topological groups
نویسندگان
چکیده
منابع مشابه
The Baire Category Theorem in Products of Linear Spaces and Topological Groups
A space is a Bake space if the intersection of countably many dense open sets is dense. We show that if X is a non-separable completely met&able linear space (pathconnected abelian topological group) then X contains two linear subspaces (subgroups) E and F such that both E and F are Baire but E x F is not. If X is a completely met&able linear space of weight K, then X is the direct sum E@F of t...
متن کاملOn the Baire Category Theorem
Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...
متن کاملProducts of Baire Spaces
Only the usual axioms of set theory are needed to prove the existence of a Baire space whose square is not a Baire space. Assuming the continuum hypothesis (CH), Oxtoby [9] constructed a Baire space whose square is not Baire. We will show in this paper that the assumption of CH is unnecessary. Such results are greatly enhanced by Krom [5], who showed that if there is such an example, then there...
متن کاملAn analogue of the Baire category theorem
Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.
متن کاملBaire category theorem and its consequences
In this notes we talk about the Baire category theorem and its consequences: the BanachSteinhaus theorem, the open mapping theorem and the closed graph theorem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1986
ISSN: 0166-8641
DOI: 10.1016/0166-8641(86)90025-8