Concerning Continuous Images of Compact Ordered Spaces
نویسنده
چکیده
It is the purpose of this paper to prove that if each of X and Y is a compact Hausdorff space containing infinitely many points, and X X Y is the continuous image of a compact ordered space L, then both X and Fare metrizable.2 The preceding theorem is a generalization of a theorem [l ] by Mardesic and Papic, who assume that X, Y, and L are also connected. Young, in [3], shows that the Cartesian product of a "long" interval and a real interval is not the continuous image of any compact ordered space. In this paper, the word compact is used in the "finite cover" sense. The phrase "ordered space" means a totally ordered topological space with the order topology. A subset M of a topological space is said to be heriditarily separable provided each subset of M is separable. If a and b are points of an ordered space L and a, and (2) {a, b} =M[a, b], provided there is one.
منابع مشابه
Ju n 20 07 A classification of CO spaces which are continuous images of compact ordered spaces 1
A topological space X is called a CO space, if every closed subset of X is homeomorphic to some clopen subset of X. Every ordinal with its order topology is a CO space. This work gives a complete classification of CO spaces which are continuous images of compact ordered spaces. 1 AMS Subject Classification 2000: Primary 06E05. Secondary 54G12, 06A05
متن کاملOn rarely generalized regular fuzzy continuous functions in fuzzy topological spaces
In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.
متن کاملThe Monad of Probability Measures over Compact Ordered Spaces and its Eilenberg-Moore Algebras
The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...
متن کاملLinearly Ordered Radon-nikodým Compact Spaces
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...
متن کامل