21 research outputs found
Primal spaces and quasihomeomorphisms
No full textIn [3], the author has introduced the notion of primal spaces.
The present paper is devoted to shedding some light on relations between quasihomeomorphisms and primal spaces.
Given a quasihomeomorphism q from X to Y , where X and Y are principal spaces, we are concerned specically with a main problem: what additional conditions have to be imposed on q in order to render X (resp.Y ) primal when Y (resp.X) is primal
On some properties of -ordered reflection
No full textIn [12], the authors give an explicit construction of the T0−ordered reflection of an ordered topological space (X, τ,≤) . All ordered topological spaces such that whose T0−ordered reflections are T1−ordered spaces are characterized. In this paper, some properties of the T0−ordered reflection of a given ordered topological space (X, τ,≤) are studies. The class of morphisms in ORDTOP orthogonal to all T0−ordered topological space is characterized
The hull orthogonal of the unit inteval [0,1]
No full textIn this paper, the full subcategory Hcomp of Top whose objects are Hausdorff compact spaces is identified as the orthogonal hull of the unit interval I = [0,1]. The family of continuous maps rendered invertible by the reflector β◦ρ is deduced
Quasihomeomorphisms and lattice equivalent topological spaces
No full textThis paper deals with lattice-equivalence of topologica lspaces. We are concerned with two questions: the first one is when two topological spaces are lattice equivalent; the second one is what additional conditions have to be imposed on lattice equivalent spaces in order that they be homeomorphic. We give a contribution to the study of these questions. Many results of Thron [Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679] are recovered, clarified and commented
Some new separation axioms in GenTop
No full textIn this paper, we introduce some new separation axioms in the category of generalized topological spaces. Some characterizations of these axioms are given. Morphisms rendered invertible by the T 0 -reflection in GenTop are entirely deter- mined. Finally, some known results in the category Top are deduced
F-n-resolvable spaces and compactifications
No full textA topological space is said to be resolvable if it is a union of
two disjoint dense subsets. More generally it is called n-resolvable if it is a union of n pairwise disjoint dense subsets. In this paper, we characterize topological spaces such that their reflections (resp., compactifications) are n-resolvable (resp., exactly-n-resolvable, strongly-exactly-n-resolvable), for some particular cases of reflections and compactifications
F-door spaces and F-submaximal spaces
No full textSubmaximal spaces and door spaces play an enigmatic role in topology. In this paper, reinforcing this role, we are concerned with reaching two main goals:
The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor Ff rom the category Top to itself. T0, and FH functors are completely studied.
Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f) in the category Set, such that (X,P(f)) is submaximal (resp., door) where P(f) is a topology on X whose closed sets are exactly the f-invariant sets
T(α,β)-spaces and the Wallman compactification
No full textSome new separation axioms are introduced and studied. We also deal
with maps having an extension to a homeomorphism between the
Wallman compactifications of their domains and ranges
