## 77 Citations

### Hausdorff separation in categories

- Mathematics, PhilosophyAppl. Categorical Struct.
- 1993

Considering subobjects, points and a closure operator in an abstract category, we introduce a generalization of the Hausdorff separation axiom for topological spaces: the notion ofT2-object. We…

### Categorically Proper Homomorphisms of Topological Groups

- MathematicsAppl. Categorical Struct.
- 2016

The Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level are extended and the stability properties of the newly defined types of maps are studied to compare them with their counterparts in topology.

### A notion of compactness in topological categories

- Mathematics
- 2005

In this paper, the notion of compactness as well as the notion of compact pairs for an arbitrary topological category is introduced. Furthermore, various generalizations of Tychonoff (completely…

### On categorical notions of compact objects

- MathematicsAppl. Categorical Struct.
- 1996

This paper introduces and studies an internal notion of compact objects relative to a closure operator and a notion of Compact objects with respect to a class of morphisms and shows that, in convenient settings, compactness can be viewed as Borel-Lebesgue compactness for a suitable closure operator.

### A categorical review of complete regularity

- Mathematics
- 2022

We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr’s Set-based relational T -algebras, and then to Burroni’s T…

### Fuzzy Compactness Via Categorical Closure Operators

- Mathematics
- 2003

The Kuratowski-Mrowka result [12, 15] that a topological space X is compact if and only if the second projection map π Y : X × Y → Y is closed for each topological space Y, has led to a number of…

### TOPOLOGY IN A CATEGORY: COMPACTNESS

- Mathematics
- 1996

In a category with a subobject structure and a closure operator, we provide a categorical theory of compactness and perfectness which yields a number of classical results of general topology as…

### Categorical compactness for rings

- MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- 1995

Abstract In this paper we study categorical compactness with respect to a class of objects F being motiveated by examples arising from modules, abelian groups, and various classes of non-abelian…

### Extremally Disconnected Compact Hausdorff Reflection

- Mathematics
- 1992

The rounding of o‐filters is introduced and this concept is used to construct an extremally disconnected compact Hausdorff reflection for a given extremally disconnected space. Some characterizations…

## References

SHOWING 1-10 OF 10 REFERENCES

### An elementary theory of the category of topological spaces

- Mathematics
- 1970

An elementary system of axioms was given by F. W. Lawvere for the category of sets and mappings. The purpose of this paper is to provide a finite number of elementary axioms for the category of…

### MACHINES IN A CATEGORY: AN EXPOSITORY INTRODUCTION*

- Computer Science, Mathematics
- 1974

A general definition of machines in an arbitrary category which unifies the theories of sequential machines, linear control systems, tree automata and stochastic automata is presented and a new fundamental realization theorem is proved which shows how to construct a broad variety of machines with prescribed behavior.

### Introduction to the Theory of Abstract Algebras

- Education
- 1968

Bargaining with reading habit is no need. Reading is not kind of something sold that you can take or not. It is a thing that will change your life to life better. It is the thing that will give you…