Countable And Uncountable Covers
Countable and Uncountable covers.
Countable Compact Scattered T₂ Spaces and Weak Forms of AC
We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T₂ space...
Disconnecting Sets and Decomposition Theories
Discrete subsets in Hausdorff topoligies.
Each concrete category has a representation by paracompact topological spaces
Eine Kennzeichnung topologischer Räume durch Vervollständigungen.
Embedding in - spaces
Epimorphims and cowellpoweredness of epireflective subcategories of Top
Epireflections in the category of -spaces
Espais essencialment TDD, TF, TY, TYS i TL.
In this paper, by means of the essential derived operator, the classes of topological spaces whose T0 identification spaces are TDD, TF, TY or TL are characterized. This classes are related with the classes of essentially-T1-spaces (R0 spaces), essentially-TD-spaces and essentially-TUD-spaces, already known.In this way, we introduce several axioms more general than the axioms between T1 and T0 defined by Aull and Thron, all of them weaker than R0.
Essentially Complete T...-Spaces.
Essentially Complete T...-Spaces II. A Lattice-Theoretic Approach.
Extremally disconnected resolutions of -spaces
Finite commutative monoids of open maps
Finite -spaces and universal mappings
Function spaces and adjoints.
Functionally Hausdorff spaces
Further remarks on KC and related spaces
A topological space is KC when every compact set is closed and SC when every convergent sequence together with its limit is closed. We present a complete description of KC-closed, SC-closed and SC minimal spaces. We also discuss the behaviour of the finite derived set property in these classes.
-closed sets and a new separation axiom in Alexandroff spaces
In this paper we introduce the concept of -closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open. We also introduce a new separation axiom called -axiom in the Alexandroff spaces with the help of -closed sets and investigate some of its consequences.