Topologies Generated by Closed Intervals
نویسندگان
چکیده
If 〈L, <〉 is a dense linear ordering without end points and A and B disjoint dense subsets of L, then the topology OAB on the set L generated by closed intervals [a, b], where a ∈ A and b ∈ B, is finer than the standard topology, O<, generated by all open intervals and 〈L,OAB〉 is a GO-space. The basic properties of the topology OAB (separation axioms, cardinal functions, metrizability) are investigated and compared with the corresponding results concerning the standard topology. AMS Mathematics Subject Classification (2000): 54F05, 03E35, 03E75, 54A10, 54A25, 54D15
منابع مشابه
Weak Topologies for the Closed Subsets of a Metrizable Space
The purpose of this article is to propose a unified theory for topologies on the closed subsets of a metrizable space. It can be shown that all of the standard hyperspace topologies—including the Hausdorff metric topology, the Vietoris topology, the Attouch-Wets topology, the Fell topology, the locally finite topology, and the topology of Mosco convergence—arise as weak topologies generated by ...
متن کاملPreorder Relators and Generalized Topologies
In this paper we investigate generalized topologies generated by a subbase of preorder relators and consider its application in the concept of the complement. We introduce the notion of principal generalized topologies obtained from the new type of open sets and study some of their important properties.
متن کاملOn Generalized Injective Spaces in Generalized Topologies
In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...
متن کاملFuzzy Topology Generated by Fuzzy Norm
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...
متن کاملTopologies generated by ideals
A topological space X is said to be generated by an ideal I if for all A ⊆ X and all x ∈ A there is E ⊆ A in I such that x ∈ E, and is said to be weakly generated by I if whenever a subset A of X contains E for every E ⊆ A with E ∈ I, then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Haus...
متن کامل