scholarly journals Topological Approaches for Rough Continuous Functions with Applications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
A. S. Salama ◽  
A. Mhemdi ◽  
O. G. Elbarbary ◽  
T. M. Al-shami
Keyword(s):  
Continuous Functions ◽  
Patient Classification ◽  
Topological Structures ◽  
Basic Properties ◽  
Lower And Upper Approximations

In this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood approach of rough functions. We generalized rough functions to topological rough continuous functions by different topological structures. In addition, topological approximations of a function as a relation were defined and studied. Finally, we applied our approach of rough functions in finding the images of patient classification data using rough continuous functions.

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

scholarly journals The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

2013 ◽  
Vol 21 (3) ◽  
pp. 185-191
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Real Banach Space ◽  
Closed Interval ◽  
Continuous Functions ◽  
Real Numbers ◽  
Riemann Integral ◽  
Basic Properties ◽  
Bounded Functions ◽  
Definition Of

Summary In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

scholarly journals Quasi cl-supercontinuous functions and their function spaces

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
J. K. Kohli ◽  
Jeetendra Aggarwal
Keyword(s):  
Continuous Functions ◽  
Function Spaces ◽  
Strong Form ◽  
General Topology ◽  
Regular Space ◽  
Basic Properties ◽  
New Class ◽  
Mathematical Literature ◽  
Class Of Functions ◽  
Appl Math

AbstractA new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi

scholarly journals TWISTED TOPOLOGICAL STRUCTURES RELATED TO M-BRANES

2011 ◽  
Vol 08 (05) ◽  
pp. 1097-1116 ◽  
Author(s):  
HISHAM SATI
Keyword(s):  
Orthogonal Group ◽  
Topological Structures ◽  
Basic Properties

Studying the M-branes leads us naturally to new structures that we call Membrane-, Membranec, StringK(ℤ,3) and FivebraneK(ℤ,4) structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tower of the orthogonal group, and demonstrate the relations to M-branes.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals On Topological Structures of Fuzzy Parametrized Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Serkan Atmaca ◽  
İdris Zorlutuna
Keyword(s):  
Topological Structure ◽  
Topological Spaces ◽  
Soft Sets ◽  
Topological Structures ◽  
Basic Properties

We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

scholarly journals Topological Structures of Lower and Upper Rough Subsets in a Hyperring

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Nabilah Abughazalah ◽  
Naveed Yaqoob ◽  
Kiran Shahzadi
Keyword(s):  
Rough Sets ◽  
Topological Spaces ◽  
Topological Structures ◽  
Lower And Upper Approximations

In this paper, we study the connection between topological spaces, hyperrings (semi-hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi-hypergroups. We provide the conditions for the boundary of hyp-ideals of a hyp-ring to become the hyp-ideals of hyp-ring.

scholarly journals CONTRA_σgμ - CONTINUOUS FUNCTIONS

2019 ◽  
Vol 1 (2) ◽  
pp. 6-9
Author(s):  
Baby K
Keyword(s):  
Continuous Functions ◽  
Basic Properties

In this paper we introduce and discuss some basic properties of contra_σgμ -continuous functions.

scholarly journals Fuzzy soft metric and fuzzifying soft topology induced by fuzzy soft metric

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 645-653
Author(s):  
Abdülkadir Aygünoğlu ◽  
Ebru Aydoğdu ◽  
Halis Aygün
Keyword(s):  
Set Theory ◽  
Metric Spaces ◽  
Soft Set ◽  
Topological Structures ◽  
Basic Properties ◽  
Soft Topology

Our main goal with this paper is to construct soft topology and fuzzifying soft topology induced by fuzzy soft metric. For this, we present fuzzy soft metric spaces compatible to soft set theory and studied some of its basic properties. Then we investigate soft topological structures induced by fuzzy soft metrics.

Sign in / Sign up

Export Citation Format

Share Document