-regular Cauchy completions.
-topological and -regular: Dual notions in convergence theory.
-topological Cauchy completions.
Pairwise fuzzy connectedness between fuzzy sets
In this paper the concept of fuzzy connectedness between fuzzy sets is generalized to fuzzy bitopological spaces and some of its properties are studied.
Pairwise fuzzy irresolute mappings
In this paper the concepts of fuzzy irresolute and fuzzy presemiopen mappings due to Yalvac [12] are generalized to fuzzy bitopological spaces and their basic properties and characterizations are studied.
Paracompact Topological Groups and Uniform Continuity
Paracompactness in box products
Partial dcpo’s and some applications
We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces , the corresponding partial dcpo’s of continuous real valued functions on are continuous partial dcpos; (iii) if a space is Hausdorff compact, the lattice of all S-lower semicontinuous functions on is the dcpo-completion of that of continuous real valued...
Partial discretization of topologies
In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.
Partial Fuzzy Metric Space and Some Fixed Point Results
In this paper, we introduce the concept of partial fuzzy metric on a nonempty set and give the topological structure and some properties of partial fuzzy metric space. Then some fixed point results are provided.
Partition properties of ω1 compatible with CH
A combinatorial statement concerning ideals of countable subsets of ω is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω, ω*)-gaps are Hausdorff, and that every coherent sequence on ω either almost includes or is orthogonal to some uncountable subset of ω.
Partitioning bases of topological spaces
We investigate whether an arbitrary base for a dense-in-itself topological space can be partitioned into two bases. We prove that every base for a Lindelöf topology can be partitioned into two bases while there exists a consistent example of a first-countable, 0-dimensional, Hausdorff space of size and weight which admits a point countable base without a partition to two bases.
P-embedding and product spaces
Point character of uniformities and completeness
Point-countable π-bases in first countable and similar spaces
It is a classical result of Shapirovsky that any compact space of countable tightness has a point-countable π-base. We look at general spaces with point-countable π-bases and prove, in particular, that, under the Continuum Hypothesis, any Lindelöf first countable space has a point-countable π-base. We also analyze when the function space has a point-countable π -base, giving a criterion for this in terms of the topology of X when l*(X) = ω. Dealing with point-countable π-bases makes it possible...
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Pointwise convergence fails to be strict
It is known that the ring of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of which differs from .
Pointwise density topology
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density...
Polars on closure spaces