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 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 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 On points of extreme chaos for almost continuous functions

2015 ◽  
Vol 62 (1) ◽  
pp. 151-164
Author(s):  
Ryszard J. Pawlak
Keyword(s):  
Continuous Functions ◽  
Point Property ◽  
Basic Properties ◽  
Dual Notion ◽  
Almost Continuous

Abstract In this paper, we introduce a new notion: extremely chaotic point and, moreover, a dual notion: family of functions having extremely chaotic point property. The basic properties of such a kind of families of functions will be considered.

scholarly journals Operation on Fine Topology

2019 ◽  
Vol 12 (3) ◽  
pp. 960-977
Author(s):  
P. L. Powar ◽  
Baravan Asaad ◽  
K. Rajak ◽  
R. Kushwaha
Keyword(s):  
Continuous Functions ◽  
Fine Topology ◽  
Basic Properties ◽  
Closed Sets ◽  
Separation Axioms

This paper introduces the concept of an operation $\gamma$ on $\tau_f$. Using this operation, we define the concept of $f_\gamma$-open sets, and study some of their related notions. Also, we introduce the concept of $f_\gamma g$.closed sets and then study some of its properties. Moreover, we introduce and investigate some types of $f_\gamma$-separation axioms and $f_{\gamma\beta}$-continuous functions by utilizing the operation $\gamma$ on $\tau_f$. Finally, some basic properties of functions with $f_\beta$-closed graphs have been obtained.

On the Essence and Tipology of International Public Goods

2005 ◽  
pp. 131-141
Author(s):  
V. Mortikov
Keyword(s):  
Economic Policy ◽  
Social Construction ◽  
Public Goods ◽  
Public Good ◽  
Global Public Goods ◽  
Club Goods ◽  
Basic Properties ◽  
International Public Goods ◽  
Regional Public Goods ◽  
Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

The advancement of silicon-on-insulator (SOI) devices and their basic properties

2020 ◽  
Vol 23 (3) ◽  
pp. 227-252
Author(s):  
T.E. Rudenko ◽  
◽  
A.N. Nazarov ◽  
V.S. Lysenko ◽  
◽  
...  
Keyword(s):  
Silicon On Insulator ◽  
Basic Properties ◽  
Soi Devices

Basic Properties of an Ultrasonic Probe with a Through Hole for Puncture and Detection Principle of a Puncture Needle

2012 ◽  
Vol 132 (11) ◽  
pp. 420-424 ◽  
Author(s):  
Yuusuke Tanaka ◽  
Katsuhiko Tanaka ◽  
Susumu Sugiyama ◽  
Hisanori Shiomi ◽  
Yoshimasa Kurumi ◽  
...  
Keyword(s):  
Ultrasonic Probe ◽  
Basic Properties ◽  
Puncture Needle ◽  
Through Hole ◽  
Detection Principle
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