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Locally ordered topological spaces

Pikul Piotr

Reports on Mathematical Logic

2020

Vol. 55

113--141

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and separation axioms and give characterisation of those regularly locally ordered spaces which are connected, locally connected or Lindel¨of. We prove that local orderability is hereditary on open, connected or compact subsets. A collection of interesting examples is also offered.

On soft pc-separation axioms

Hamko Qumri H., Ahmed Nehmat K., Khalaf Alias B.

Demonstratio Mathematica

2020

Vol. 53, nr 1

67--79

Many mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological space X. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft pc−Ti and soft pc−T⁎i, i=0,1,2 by using the concept of soft pc-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.

Almost continuity, regular set-connected mappings and some separation axioms

Duszyński Z.

Demonstratio Mathematica

2006

Vol. 39, nr 4

939-948

Let f : (X, r ) approaches (Y,sigma) be a mapping, let (X, rs) denote the topological space generated by the family of all regular open subsets of (X, r ) and let fxs : (X, rs) !approaches (Y, sigma) be defined by fxs (x) = f(x) for each x is an element of X. In the paper relationships between almost continuity of f, almost continuity of fxs and some other types of mappings (r.s.c. mappings in particular) are studied.

Higher separation axioms in generalized closure spaces

Stadler B. M. R., Stadler P. F.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

[Z] 43(2)

257-273

The hierarchy of separation axioms that is familiar from topological spaces generalizes to spaces with an isotone and expansive closure function. Neither additivity nor idempotence of the closure function must be assumed.

On density topologies with respect to invariant σ-ideals

Hejduk J.

Journal of Applied Analysis

2002

Vol. 8, nr 2

201-219

The density topologies with respect to measure and category are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied.