On Hereditary Coreflective Subcategories of Top
نویسنده
چکیده
Let A be a topological space which is not finitely generated and CH(A) denote the coreflective hull of A in Top. We construct a generator of the coreflective subcategory SCH(A) consisting of all subspaces of spaces from CH(A) which is a prime space and has the same cardinality as A. We also show that if A and B are coreflective subcategories of Top such that the hereditary coreflective kernel of each of them is the subcategory FG of all finitely generated spaces, then the hereditary coreflective kernel of their join CH(A ∪B) is again FG.
منابع مشابه
Hereditary, Additive and Divisible Classes in Epireflective Subcategories of Top
Martin Sleziak HAD-classes in epireflective subcategories of Top Introduction Heredity of AD-classes References Basic definitions Hereditary coreflective subcategories of Top A generalization – epireflective subcategories AD-classes and HAD-classes Subcategories of Top All subcategories are assumed to be full and isomorphism-closed. subcategory of Top = class of topological spaces closer under ...
متن کاملUNIVERZITA KOMENSKÉHO V BRATISLAVE FAKULTA MATEMATIKY, FYZIKY A INFORMATIKY Katedra algebry, geometrie a didaktiky matematiky HEREDITY, HEREDITARY COREFLECTIVE HULLS AND OTHER PROPERTIES OF COREFLECTIVE SUBCATEGORIES OF CATEGORIES OF TOPOLOGICAL SPACES
This thesis deals mainly with hereditary coreflective subcategories of the category Top of topological spaces. After preparing the basic tools used in the rest of thesis we start by a question which coreflective subcategories of Top have the property SA = Top (i.e., every topological space can be embedded in a space from A). We characterize such classes by finding generators of the smallest cor...
متن کاملProductivity of coreflective classes of topological groups
Every nontrivial countably productive coreflective subcategory of topological linear spaces is κ-productive for a large cardinal κ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal κ, there are coreflective subcategories that are κ-productive and not κ-productive (see [8]). From certain points of view, the category of topological groups lies in between those ca...
متن کاملSubspaces of pseudoradial spaces
We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1-space). This answers the Problem 3 in [2]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top.
متن کاملCategory and subcategories of (L,M)-fuzzy convex spaces
Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Categorical Structures
دوره 12 شماره
صفحات -
تاریخ انتشار 2004