On a problem concerning generalizations of realcompact spaces
نویسندگان
چکیده
منابع مشابه
Maximal Realcompact Spaces and Measurable Cardinals
Comfort and Hager investigate the notion of a maximal realcompact space and ask about the relationship to the first measurable cardinal m. A space is said to be a P (m) space if the intersection of fewer than m open sets is again open. They ask if each realcompact P (m) space is maximal realcompact. We establish that this question is undecidable.
متن کاملLocally realcompact and HN-complete spaces
Two classes of spaces are studied, namely locally realcompact spaces and HNcomplete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences ...
متن کاملOn a Problem concerning Permutation Polynomials
Let S(f) denote the set of integral ideals / such that / is a permutation polynomial modulo i", where / is a polynomial over the ring of integers of an algebraic number field. We obtain a classification for the sets S which may be written in the form S(f). Introduction. A polynomial f(x) with coefficients in a commutative ring R is said to be a permutation polynomial modulo an ideal I oi R (abb...
متن کاملOn A Problem Concerning Parameter Free Induction
8 0. Preliminaries In this note we comment on the relationships among local versions of the parameter free induction, collection and pigeonhole schemas. We start by defining the versions that will interest us. We work in the usual language of arithmetic to which a new constant symbol a has been added. P-denotes a finite set of axioms such that if M C P-, then M is the nonnegative part of a comm...
متن کاملOn a Problem Concerning the Weight Functions
Let X be a finite set with n elements. A function f : X −→ R such that ∑ x∈X f (x) ≥ 0 is called a n-weight function. In 1988 Manickam and Singhi conjectured that, if d is a positive integer and f is a n-weight function with n ≥ 4d there exist at least (n−1 d−1 ) subsets Y of X with |Y | = d for which ∑ y∈Y f (y) ≥ 0. In this paper we study this conjecture and we show that it is true if f is a ...
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: 1983
ISSN: 0166-8641
DOI: 10.1016/0166-8641(83)90013-5