Add to ORKGA topological space is called resolvable if it is a union of two disjoint dense subsets, and is n-resolvable if it is a union of n mutually disjoint dense subsets. Clearly a resolvable space has no isolated points. If ƒ is a selfmap on X, the sets A ⊆ X with ƒ(A) ⊆ A are the closed sets of an Alexandroff topology called the primal topology Ρ(ƒ) associated with ƒ. We investigate resolvability for primal spaces (X;Ρ(ƒ)). Our main result is that an Alexandroff space is resolvable if and only if it has no isolated points. Moreover, n-resolvability and other related concepts are investigated for primal spaces.Mathematics Subject Classication (2010): 54B25, 18B30.Key words: Primal spaces, categories, resolvable spaces
AbstractA nonempty topological space is resolvable if it contains two complementary dense subsets. T...
AbstractIn a recent paper O. Pavlov proved the following two interesting resolvability results:(1)If...
AbstractA topological space X is called strongly exactly n-resolvable if X is n-resolvable and no no...
Alexandroff topologies play an enigmatic role in topology. An important family of Alexandroff topolo...
AbstractFollowing guidance from the Organizing Committee, the authors give a brief introduction to t...
Given an innite set X and a function f : X→ X, the primal topology on X induced by f is the topology...
AbstractResolvability of spaces whose extent (spread) is less than the dispersion character is inves...
A topological space is said to be resolvable if it is a union of two disjoint dense subsets. More ge...
Abstract. The notion of the resolvability of a topological space was introduced by E. Hewitt [8]. Re...
AbstractWe show that a T1 space X is resolvable if the set of limit points λ (X) of various simultan...
AbstractThe formation of maximal topologies and the use of maximal independent families are the only...
In this paper some properties of open hereditarily irresolvable spaces are obtained and the topology...
summary:We show a new theorem which is a sufficient condition for maximal resolvability of a topolog...
summary:We prove resolvability and maximal resolvability of topological spaces having countable tigh...
summary:It is proved that every uncountable $\omega$-bounded group and every homogeneous space conta...
AbstractA nonempty topological space is resolvable if it contains two complementary dense subsets. T...
AbstractIn a recent paper O. Pavlov proved the following two interesting resolvability results:(1)If...
AbstractA topological space X is called strongly exactly n-resolvable if X is n-resolvable and no no...
Alexandroff topologies play an enigmatic role in topology. An important family of Alexandroff topolo...
AbstractFollowing guidance from the Organizing Committee, the authors give a brief introduction to t...
Given an innite set X and a function f : X→ X, the primal topology on X induced by f is the topology...
AbstractResolvability of spaces whose extent (spread) is less than the dispersion character is inves...
A topological space is said to be resolvable if it is a union of two disjoint dense subsets. More ge...
Abstract. The notion of the resolvability of a topological space was introduced by E. Hewitt [8]. Re...
AbstractWe show that a T1 space X is resolvable if the set of limit points λ (X) of various simultan...
AbstractThe formation of maximal topologies and the use of maximal independent families are the only...
In this paper some properties of open hereditarily irresolvable spaces are obtained and the topology...
summary:We show a new theorem which is a sufficient condition for maximal resolvability of a topolog...
summary:We prove resolvability and maximal resolvability of topological spaces having countable tigh...
summary:It is proved that every uncountable $\omega$-bounded group and every homogeneous space conta...
AbstractA nonempty topological space is resolvable if it contains two complementary dense subsets. T...
AbstractIn a recent paper O. Pavlov proved the following two interesting resolvability results:(1)If...
AbstractA topological space X is called strongly exactly n-resolvable if X is n-resolvable and no no...