scholarly journals On pseudocompact topological Brandt λ0-extensions of semitopological monoids

2013 ◽  
Vol 1 ◽  
pp. 60-79
Author(s):  
Oleg Gutik ◽  
Kateryna Pavlyk
Keyword(s):  
Topological Properties ◽  
Countably Compact ◽  
Compact Extension

AbstractIn the paper we investigate topological properties of a topological Brandt λ0-extension B0λ(S) of a semitopological monoid S with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid S with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension B0λ(S) of S and establish their Stone-Cˇ ech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt λ0- extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

scholarly journals LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE

2017 ◽  
Vol 20 (10) ◽  
pp. 68-73
Author(s):  
O.I. Pavlov
Keyword(s):  
Topological Space ◽  
Normal Space ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
Countably Compact ◽  
Ordered Space ◽  
One To One ◽  
Hereditary Properties

One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

scholarly journals An ideal version of the star-C-Hurewicz covering property

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6385-6393
Author(s):  
Sumit Singh ◽  
Brij Tyagi ◽  
Manoj Bhardwaj
Keyword(s):  
Hausdorff Space ◽  
Winning Strategy ◽  
Topological Properties ◽  
Covering Property ◽  
Countably Compact ◽  
Compact Subsets

A space X is said to have the star-C-I-Hurewicz (SCIH) property if for each sequence (Un : n ? N) of open covers of X there is a sequence (Kn : n ? N) of countably compact subsets of X such that for each x ? X, {n ? N : x ? St(Kn,Un)} ? I, where I is a proper admissible ideal of N. We investigate the relationships among the SCIH and related properties. We study the topological properties of the SCIH property. This paper generalizes several results of [21, 24] to the larger class of spaces having the SCIH property. The star-C-I-Hurewicz game is introduced. It is shown that, in a paracompact Hausdorff space X, if TWO has a winning strategy in the SCIH game on X, then TWO has a winning strategy in the I-Hurewicz game on X.

scholarly journals Topological properties of the scale of a uniform space

1982 ◽  
Vol 33 (1) ◽  
pp. 54-61 ◽  
Author(s):  
G. D. Richardson ◽  
E. M. Wolf
Keyword(s):  
Uniform Space ◽  
Topological Properties ◽  
Uniform Lattice ◽  
Totally Bounded ◽  
Countably Compact

AbstractLet (S. U) be a uniform space. This space can be embedded in a complete, uniform lattice called the scale of (S. U). We prove that the scale is compact if and only if S is finite or U = {S × S}. We prove that this statement remains true if compact is replaced by countably compact, totally bounded. Lindelof, second countable, or separable. In the last section of this paper, we investigate the cardinality of the scale and the retracted scale.

Some contributions to definability theory for languages with generalized quantifiers

1982 ◽  
Vol 47 (3) ◽  
pp. 572-586
Author(s):  
John T. Baldwin ◽  
Douglas E. Miller
Keyword(s):  
Order Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Natural Class ◽  
First Order ◽  
First Order Theory ◽  
First Results ◽  
Countably Compact ◽  
Compact Extension ◽  
Almost All

One of the first results in model theory [12] asserts that a first-order sentence is preserved in extensions if and only if it is equivalent to an existential sentence.In the first section of this paper, we analyze a natural program for extending this result to a class of languages extending first-order logic, notably including L(Q) and L(aa), respectively the languages with the quantifiers “there exist un-countably many” and “for almost all countable subsets”.In the second section we answer a question of Bruce [3] by showing that this program cannot resolve the question for L(Q). We also consider whether the natural class of “generalized Σ-sentences” in L(Q) characterizes the class of sentences preserved in extensions, refuting the relativized version but leaving the unrestricted question open.In the third section we show that the analogous class of L(aa)-sentences preserved in extensions does not include (up to elementary equivalence) all such sentences. This particular candidate class was nominated, rather tentatively, by Bruce [3].In the fourth section we show that under rather general conditions, if L is a countably compact extension of first-order logic and T is an ℵ1-categorical first-order theory, then L is trivial relative to T.

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.

SOME TOPOLOGICAL PROPERTIES OF HAMEL BASES

1994 ◽  
Vol 20 (2) ◽  
pp. 819
Author(s):  
Muthuvel
Keyword(s):  
Topological Properties

scholarly journals DNA thermodynamics shape chromosome organization and topology

2013 ◽  
Vol 41 (2) ◽  
pp. 548-553 ◽  
Author(s):  
Andrew A. Travers ◽  
Georgi Muskhelishvili
Keyword(s):  
Dna Sequence ◽  
Dna Sequences ◽  
Chromosome Organization ◽  
Topological Properties ◽  
Genetic Organization ◽  
And Topology ◽  
Dna Translocases

How much information is encoded in the DNA sequence of an organism? We argue that the informational, mechanical and topological properties of DNA are interdependent and act together to specify the primary characteristics of genetic organization and chromatin structures. Superhelicity generated in vivo, in part by the action of DNA translocases, can be transmitted to topologically sensitive regions encoded by less stable DNA sequences.

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