New forms of separation spaces in bitopology

The aim of this paper is to study how distinct points and a point and a closed set not containing that points are separated by non overlapping open neighborhoods, in a bitopological space. The separation is studied with respect to a new type of $(1,2)\alpha$-open set together with a continuous function. We named the new axioms as star-ultra $T_{1}$, star-ultra $T_{2}$, star-ultra regular and normal. The star-ultra regular spaces is studied in two different ways and are called as A-star-ultra regular and B-star-ultra regular spaces.

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A new type of generalized closed set via γ-open set in a fuzzy bitopological space

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-2019-03-0033 ◽

2019 ◽

Vol 38 (3) ◽

pp. 511-536 ◽

Cited By ~ 1

Author(s):

Birojit Das ◽

Baby Bhattacharya ◽

Jayasree Chakaraborty ◽

Sree Anusha Ganapathiraju ◽

Arnab Paul

Keyword(s):

Bitopological Space ◽

Closed Set ◽

Open Set ◽

New Type

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On pairwise $\mathcal{N}$-$\beta$-open sets in bitopological spaces

Journal of Advanced Studies in Topology ◽

10.20454/jast.2016.1099 ◽

2016 ◽

Vol 7 (3) ◽

pp. 152

Author(s):

Fahad Alsharari ◽

Abdo Qahis

Keyword(s):

Continuous Function ◽

Open Cover ◽

Bitopological Space ◽

Open Set ◽

Bitopological Spaces

In this paper, we introduce the notion of an $(i,j)$-$\mathcal{N}$-$\beta$-open set which is a generalization of an $(i,j)$-$\beta$-open set in a bitopological space. Also, we investigate some of its properties and characterizations. Besides, we prove that a pairwise $(i, j)$-$\mathcal{N}$-$\beta$-open cover that has a finite (countable) subcover is equivalent to a pairwise $\beta$-compact ($\beta$-Lindel\"{ö}f) space. Finally, we introduce an $(i, j)$-$\mathcal{N}$-$\beta$-continuous function and an $(i, j)$-$\mathcal{N}$-$\beta$-irresolute function and obtain some of their properties.

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On T1 T2-g-Open Sets in Bitopological Spaces

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2019/v34i230216 ◽

2019 ◽

pp. 1-8

Author(s):

K. Vithyasangaran ◽

P. Elango ◽

S. Sathaananthan ◽

J. Sriranganesan ◽

P. Paramadevan

Keyword(s):

Continuous Function ◽

Topological Spaces ◽

Bitopological Space ◽

Open Set ◽

Bitopological Spaces

In this paper, we introduced and studied a new kind of generalized open set called τ1τ2-g-open set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-g-open set are studied and compared with some of the corresponding generalized open sets in general topological spaces and bitopological spaces. We also dened the τ1τ2-g-continuous function and studied some its properties.

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On Strongly b − θ -Continuous Mappings in Fuzzifying Topology

Mathematical Problems in Engineering ◽

10.1155/2021/3244618 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Ting Yang ◽

Ahmed Mostafa Khalil

Keyword(s):

Fuzzy Logic ◽

Continuous Mapping ◽

Topological Spaces ◽

Closed Set ◽

Open Set ◽

Neighborhood System ◽

Continuous Mappings ◽

Derived Set ◽

New Type

In this article, we will define the new notions (e.g., b − θ -neighborhood system of point, b − θ -closure (interior) of a set, and b − θ -closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of the above five notions in detail. Several basic results (for instance, Definition 7, Theorem 3 (iii), (v), and (vi), Theorem 5, Theorem 9, and Theorem 4.6) in classical topology are generalized in fuzzy logic. In addition to, we will show that every fuzzifying b − θ -closed set is fuzzifying γ -closed set (by Theorem 3 (vi)). Further, we will study the notion of fuzzifying b − θ -derived set and fuzzifying b − θ -boundary set and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly b − θ -continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly b − θ -continuous mapping, fuzzifying strongly b − θ -irresolute mapping, and fuzzifying weakly b − θ -irresolute mapping along with different conditions for their existence are obtained.

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Neutrosophic Soft Bitopological Spaces

International Journal of Neutrosophic Science ◽

10.54216/ijns.140104 ◽

2021 ◽

Author(s):

Ahmed B. AL-Nafee ◽

◽

Said Broumi ◽

Florentin Smarandache ◽

◽

...

Keyword(s):

Soft Set ◽

Topological Spaces ◽

Bitopological Space ◽

Closed Set ◽

Open Set ◽

Bitopological Spaces

In this paper, we built bitopological space on the concept of neutrosophic soft set, we defined the basic topological concepts of this spaces which are N3-(bi)*-open set, N3-(bi)*-closed set, (bi)*-neutrosophic soft interior, (bi)* neutrosophic soft closure, (bi)*-neutrosophic soft boundary, (bi)*-neutrosophic soft exterior and we introduced their properties. In addition, we investigated the relations of these basic topological concepts with their counterparts in neutrosophic soft topological spaces and we introduced many examples.

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DISCUSSION ON QUOTIENT BI-SPACE AND ON PAIRWISE REGULAR AND NORMAL SPACES IN BITOPOLOGICAL SPACES

Advances in Mathematical Sciences ◽

10.37516/adv.math.sci.2019.0051 ◽

2019 ◽

pp. 13-15

Author(s):

M. Arunmaran ◽

K. Kannan

Keyword(s):

Compact Subset ◽

Hausdorff Space ◽

Bitopological Space ◽

Closed Set ◽

Continuous Map ◽

Open Set ◽

Bitopological Spaces

In this paper, we introduce the concept “Quotient bi-space” in bitopological spaces. In addition, we investigate the results related with quotient bi-space. Moreover, we have discussed the results related with pairwise regular and normal spaces in bitopological space. For a non-empty set X, we can define two topologies (these may be same or distinct topologies) τ1 and τ2 on X. Then, the triple (X, τ1 , τ2 ) is known as bitopological space. Let (X, τ1 , τ2 ) be bitopological space, (Y, σ1 , σ2 ) be trivial bitopological space and f : (X, τ1 , τ2 ) → (Y, σ1 , σ2 ) be onto map. Then f is τ1 τ2 −continuous map. If η = {G (σ − open set in Y ) : f ^{−1} (G) is τ1 τ2 − open in X} then η is a topology on Y . Moreover, if (Y, σ, σ) be a quotient bi-space of (X, τ1 , τ2) under f : (X, τ1 , τ2 ) → (Y, σ, σ) and g : (Y, σ, σ) → (Z, η1 , η2 ) be a map, then, gis σ − continuous if and only if g ◦ f : (X, τ1 , τ2 ) → (Z, η1 , η2 ) is τ1 τ2 −continuous. Let (X, τ1 , τ2) be bitopological space and A be τ1 τ2 − compact subset of pairwise Hausdorff space X. Then, A is τ1 τ2 − closed set. Finally, we have discussed the following : Let (X, τ1 , τ2 ) be bitopological space and τ1 τ2 −compact pairwise Hausdorff space. Then, the space (X, τ1 , τ2 ) is pairwise normal.

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ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.41 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9353-9360

Author(s):

G. Selvi ◽

I. Rajasekaran

Keyword(s):

Topological Spaces ◽

Closed Set ◽

Basic Properties ◽

Closed Sets ◽

New Class ◽

Open Set ◽

Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

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Synthetic speech detection through short-term and long-term prediction traces

EURASIP Journal on Information Security ◽

10.1186/s13635-021-00116-3 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Clara Borrelli ◽

Paolo Bestagini ◽

Fabio Antonacci ◽

Augusto Sarti ◽

Stefano Tubaro

Keyword(s):

Deep Learning ◽

Speech Processing ◽

Synthetic Speech ◽

Opinion Formation ◽

Closed Set ◽

Speech Detection ◽

Open Set ◽

Technological Advances ◽

Speech Generation ◽

Long Term Prediction

AbstractSeveral methods for synthetic audio speech generation have been developed in the literature through the years. With the great technological advances brought by deep learning, many novel synthetic speech techniques achieving incredible realistic results have been recently proposed. As these methods generate convincing fake human voices, they can be used in a malicious way to negatively impact on today’s society (e.g., people impersonation, fake news spreading, opinion formation). For this reason, the ability of detecting whether a speech recording is synthetic or pristine is becoming an urgent necessity. In this work, we develop a synthetic speech detector. This takes as input an audio recording, extracts a series of hand-crafted features motivated by the speech-processing literature, and classify them in either closed-set or open-set. The proposed detector is validated on a publicly available dataset consisting of 17 synthetic speech generation algorithms ranging from old fashioned vocoders to modern deep learning solutions. Results show that the proposed method outperforms recently proposed detectors in the forensics literature.

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Mosquito species identification using convolutional neural networks with a multitiered ensemble model for novel species detection

Scientific Reports ◽

10.1038/s41598-021-92891-9 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Adam Goodwin ◽

Sanket Padmanabhan ◽

Sanchit Hira ◽

Margaret Glancey ◽

Monet Slinowsky ◽

...

Keyword(s):

Neural Networks ◽

Species Identification ◽

Convolutional Neural Networks ◽

Novel Species ◽

Novelty Detection ◽

Mosquito Species ◽

Image Database ◽

Closed Set ◽

Open Set

AbstractWith over 3500 mosquito species described, accurate species identification of the few implicated in disease transmission is critical to mosquito borne disease mitigation. Yet this task is hindered by limited global taxonomic expertise and specimen damage consistent across common capture methods. Convolutional neural networks (CNNs) are promising with limited sets of species, but image database requirements restrict practical implementation. Using an image database of 2696 specimens from 67 mosquito species, we address the practical open-set problem with a detection algorithm for novel species. Closed-set classification of 16 known species achieved 97.04 ± 0.87% accuracy independently, and 89.07 ± 5.58% when cascaded with novelty detection. Closed-set classification of 39 species produces a macro F1-score of 86.07 ± 1.81%. This demonstrates an accurate, scalable, and practical computer vision solution to identify wild-caught mosquitoes for implementation in biosurveillance and targeted vector control programs, without the need for extensive image database development for each new target region.

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