scholarly journals Some topological properties of the space of maximal linked systems with topology of Wallman type

2020 ◽  
Vol 56 ◽  
pp. 122-137
Author(s):  
A.G. Chentsov
Keyword(s):  
Measurable Space ◽  
Topological Properties ◽  
Bitopological Spaces ◽  
Space Conditions ◽  
Degenerate Cases

Maximal linked systems (MLS) and ultrafilters (u/f) on a widely understood measurable space (this is a nonempty set with equipment in the form of π-system with “zero” and “unit”) are investigated. Under equipment with topology of Wallman type, the set of MLS is converted into a supercompact T1-space. Conditions under which given space of MLS is a supercompactum (i.e., a supercompact T2-space) are investigated. These conditions then apply to the space of u/f under equipment with topology of Wallman type. The obtained conditions are coordinated with representations obtained under degenerate cases of bitopological spaces with topologies of Wallman and Stone types, but they are not the last to be exhausted.

Maximal linked systems and ultrafilters: main representations and topological properties

2020 ◽  
pp. 68-84
Author(s):  
Aleksandr G. Chentsov
Keyword(s):  
Measurable Space ◽  
Topological Properties ◽  
Bitopological Space ◽  
Measurable Structure ◽  
Bitopological Spaces ◽  
Algebras Of Sets

Questions connected with representation of the ultrafilter (UF) set for widely understood measurable space are investigated; this set is considered as a subspace of bitopological space of maximal linked systems (MLS) under equipment with topologies of Wallman and Stone types (measurable structure is defined as a π -system with “zero” and “unit”). Analogous representations connected with generalized variant of cohesion is considered also; in this variant, for corresponding set family, it is postulated the nonemptyness of intersection for finite subfamilies with power not exceeding given. Conditions of identification of UF and MLS (in the above-mentioned generalized sense) are investigated. Constructions reducing to bitopological spaces with points in the form of MLS and 𝑛-supercompactness property generalizing the “usual” supercompactness are considered. Finally, some characteristic properties of MLS and their corollaries connected with the MLS contraction to a smaller π -system are being studied. The case of algebras of sets is selected separately.

MAXIMAL LINKED SYSTEMS AND ULTRAFILTERS OF WIDELY UNDERSTOOD MEASURABLE SPACES

2018 ◽  
pp. 846-860
Author(s):  
Aleksandr Georgievich Chentsov
Keyword(s):  
Sufficient Conditions ◽  
Measurable Space ◽  
Necessary And Sufficient Conditions ◽  
Bitopological Space ◽  
Necessary And Sufficient ◽  
Bitopological Spaces

Two types of set families (ultrafilters or maximal filters and maximal linked systems) for widely understood measurable space are considered. The resulting sets of ultrafilters and maximal linked systems are equipped with the pair of comparable topologies (within the meaning of «Wallman» and «Stone»). As a result, two bitopological spaces are realized; one of them turns out a subspace of another. More precisely, ultrafilters are maximal linked systems and the totality of the latter forms a cumulative bitopological space. With employment of topological constructions some characteristic properties of ultrafilters and (in smaller power) maximal linked systems are obtained (the question is necessary and sufficient conditions of maximality of filters and linked systems).

scholarly journals Filters and linked families of sets

2020 ◽  
Vol 30 (3) ◽  
pp. 444-467
Author(s):  
A.G. Chentsov
Keyword(s):  
Measurable Space ◽  
The Family ◽  
System Product ◽  
Bitopological Spaces

Properties of ultrafilters (u/f) and maximal linked systems (MLS) on the widely understood measurable space (MS) and representations of linked (not necessarily maximal) families and filters on this MS are investigated. Conditions realizing maximality of linked families (systems) and natural representations for bitopological spaces (BTS) of u/f and MLS are established. Equipments of sets of linked families and filters corresponding to Wallman and Stone schemes are studied; the connection of these equipments with analogous equipments (with topologies) for u/f and MLS leading to above-mentioned BTS is studied too. Properties of linked family products for two (widely understood) MS are investigated. It is shown that MLS on the π-system product (that is, on the family of “measurable” rectangles) are limited to products of corresponding MLS on initial spaces.

scholarly journals A View on Connectedness and Compactness in Fuzzy Soft Bitopological Spaces

2021 ◽  
Vol 14 (3) ◽  
pp. 760-772
Author(s):  
Abdelhamied Farrag Sayed
Keyword(s):  
Topological Properties ◽  
Separated Sets ◽  
Bitopological Spaces

In the present paper, we introduce the notions of (1, 2)∗-fuzzy soft b-separated sets, (1, 2)∗-fuzzy soft b-connectedness and (1, 2)∗-fuzzy soft b-compactness in fuzzy soft bitopological spaces. Then, some basic topological properties of these notions are investigated. Also, some illustrative examples are given to show the importance of the obtained theorems.

scholarly journals Investigations onweak versions of the Alster property in bitopological spaces and selection principles

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4561-4571
Author(s):  
Emre Eysen ◽  
Selma Özçağ
Keyword(s):  
Topological Properties ◽  
Selection Principles ◽  
Bitopological Spaces

We investigate the relationships among the weaker forms of the properties ?Menger?, ?Alster? and ?Lindel?f? in bitopological spaces. We give some counterexamples to show the differences between these properties. Further we introduce the weak versions of the Alster property in terms of selection principles and obtain some of their topological properties.

Electron Microscopy of Nucleic Acids

1974 ◽  
Vol 32 ◽  
pp. 302-303
Author(s):  
Norman Davidson
Keyword(s):  
Electron Microscopy ◽  
Nucleic Acids ◽  
Basic Protein ◽  
Molecular Biologist ◽  
Topological Properties ◽  
Protein Film ◽  
Polynucleotide Chain

The basic protein film technique for mounting nucleic acids for electron microscopy has proven to be a general and powerful tool for the working molecular biologist in characterizing different nucleic acids. It i s possible to measure molecular lengths of duplex and single-stranded DNAs and RNAs. In particular, it is thus possible to as certain whether or not the nucleic acids extracted from a particular source are or are not homogeneous in length. The topological properties of the polynucleotide chain (linear or circular, relaxed or supercoiled circles, interlocked circles, etc. ) can also be as certained.

The Effect of Topological Properties on Duration Perception of Oddball Stimuli

2013 ◽  
Vol 45 (12) ◽  
pp. 1324-1333
Author(s):  
Baolin LI ◽  
Youguo CHEN ◽  
Xiangyong YUAN ◽  
Jackson Todd ◽  
Xiting HUANG
Keyword(s):  
Topological Properties

Molecular Topological Properties of Alkylating Agents Based Anticancer Drug Candidates Via Some Ve-degree Topological Indices

2020 ◽  
Vol 16 (2) ◽  
pp. 190-195 ◽  
Author(s):  
Süleyman Ediz ◽  
Murat Cancan
Keyword(s):  
Anticancer Drugs ◽  
Anticancer Drug ◽  
Alkylating Agents ◽  
Topological Indices ◽  
Pharmacological Properties ◽  
Topological Properties ◽  
Drug Candidates ◽  
New Drug ◽  
Atom Bond ◽  
Dual Target

Background: Reckoning molecular topological indices of drug structures gives the data about the underlying topology of these drug structures. Novel anticancer drugs have been leading by researchers to produce ideal drugs. Materials and Methods: Pharmacological properties of these new drug agents explored by utilizing simulation strategies. Topological indices additionally have been utilized to research pharmacological properties of some drug structures. Novel alkylating agents based anticancer drug candidates and ve-degree molecular topological indices have been introduced recently. Results and Conclusion: In this study we calculate ve-degree atom-bond connectivity, harmonic, geometric-arithmetic and sum-connectivity molecular topological indices for the newly defined alkylating agents based dual-target anticancer drug candidates.

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