Insertion of a Contra-continuous Function between Two Comparable Real-valued Functions

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a contra-continuous function between two comparable real-valued functions on such topological spaces that kernel of sets are open.

‎INSERTION OF A CONTRA-CONTINUOUS FUNCTION BETWEEN TWO ‎‎COMPARABLE CONTRA-$\alpha-$CONTINUOUS (CONTRA-$C-$CONTINUOUS) FUNCTIONS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1901013m ◽

2019 ◽

pp. 13

Author(s):

Majid Mirmiran ◽

Binesh Naderi

Keyword(s):

Continuous Function ◽

Continuous Functions ◽

Topological Spaces ◽

Sufficient Condition ◽

‎A necessary and sufficient condition in terms of lower cut sets ‎are given for the insertion of a contra-continuous function ‎between two comparable real-valued functions on such topological ‎spaces that kernel of sets are open‎.

Semi-smooth Points in Some Classical Function Spaces

Results in Mathematics ◽

10.1007/s00025-021-01545-9 ◽

2021 ◽

Vol 77 (1) ◽

Author(s):

Beata Derȩgowska ◽

Beata Gryszka ◽

Karol Gryszka ◽

Paweł Wójcik

Keyword(s):

Continuous Function ◽

Metric Space ◽

Continuous Functions ◽

Sufficient Condition ◽

Compact Metric Space ◽

Spaces Of Continuous Functions ◽

Classical Function ◽

Vector Valued

AbstractThe investigations of the smooth points in the spaces of continuous function were started by Banach in 1932 considering function space $$\mathcal {C}(\Omega )$$ C ( Ω ) . Singer and Sundaresan extended the result of Banach to the space of vector valued continuous functions $$\mathcal {C}(\mathcal {T},E)$$ C ( T , E ) , where $$\mathcal {T}$$ T is a compact metric space. The aim of this paper is to present a description of semi-smooth points in spaces of continuous functions $$\mathcal {C}_0(\mathcal {T},E)$$ C 0 ( T , E ) (instead of smooth points). Moreover, we also find necessary and sufficient condition for semi-smoothness in the general case.

On Weighted Polynomial Approximation With Gaps

Nagoya Mathematical Journal ◽

10.1017/s0027763000009119 ◽

2005 ◽

Vol 178 ◽

pp. 55-61 ◽

Cited By ~ 10

Author(s):

Guantie Deng

Keyword(s):

Banach Space ◽

Continuous Function ◽

Polynomial Approximation ◽

Continuous Functions ◽

Sufficient Condition ◽

Weighted Polynomial Approximation ◽

Weighted Banach Space ◽

Nonnegative Continuous Function ◽

Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.

Metrisation of Moore spaces and abstract topological manifolds

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700031178 ◽

1997 ◽

Vol 56 (3) ◽

pp. 395-401 ◽

Cited By ~ 1

Author(s):

David L. Fearnley

Keyword(s):

Recent Work ◽

Topological Spaces ◽

Sufficient Condition ◽

Moore Space ◽

Global Coherence ◽

Topological Manifolds ◽

Moore Spaces ◽

Significant Class

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.

Dunkl harmonic analysis and fundamental sets of continuous functions on the unit sphere

Advances in Pure and Applied Mathematics ◽

10.1515/apam-2014-0053 ◽

2015 ◽

Vol 6 (3) ◽

Author(s):

Roman A. Veprintsev

Keyword(s):

Continuous Function ◽

Harmonic Analysis ◽

Unit Sphere ◽

Continuous Functions ◽

Sufficient Condition ◽

The Family ◽

AbstractWe establish a necessary and sufficient condition on a continuous function on [-1,1] under which the family of functions on the unit sphere 𝕊

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

Cesàro kernels on classical groups

10.1017/s1446788700000951 ◽

1997 ◽

Vol 63 (3) ◽

pp. 364-389

Author(s):

Dashan Fan

Keyword(s):

Continuous Function ◽

Harmonic Analysis ◽

Classical Group ◽

Sufficient Condition ◽

Classical Groups ◽

Cesàro Operator ◽

Cesaro Operator

AbstractWe study the Cesàro operator on the classical group G and give a necessary and sufficient condition on the index α = α(G) for which the operator is convergent to f(U) for any continuous function f as N → ∞. The result in this paper solves a question posed by Gong in the book Harmonic analysis on classical groups.

Erratum: A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function

Dynamical Systems ◽

10.1080/1468936031000095672 ◽

2003 ◽

Vol 18 (3) ◽

pp. 271-278 ◽

Cited By ~ 2

Author(s):

P. Walters

Keyword(s):

Continuous Function ◽

Sufficient Condition ◽

Badly approximable functions and interpolation by Blaschke products

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500010671 ◽

1976 ◽

Vol 20 (2) ◽

pp. 159-161 ◽

Cited By ~ 1

Author(s):

L. A. Rubel ◽

A. L. Shields

Keyword(s):

Continuous Function ◽

Supremum Norm ◽

Sufficient Condition ◽

Blaschke Products ◽

Winding Number ◽

Uniform Limit ◽

Disc Algebra ◽

Badly Approximable

A continuous function φ on the unit circle is called badly approximable if ‖ φ − p ‖∞ ≧ ‖ φ |∞ for all polynomials p, where ‖ |∞ is the essential supremum norm. In (4), Poreda asked whether every continuous φ may be written φ = φW+φB, where φW is the uniform limit of polynomials (i.e. φW belongs to the disc algebra A) and φB is badly approximable. We call such a function φ decomposable. In (4), he characterised the badly approximable functions as those of constant non-zero modulus and negative winding number around the origin, i.e. ind (φ)<0. (See (3) for two new proofs of this result.) We show that the answer to Poreda's question is no in general, but give a necessary and sufficient condition for a given φ to have such a decomposition. Then we apply this criterion to solve an interpolation problem.

Minimal bases and minimal sub-bases for topological spaces

Filomat ◽

10.2298/fil1907957l ◽

2019 ◽

Vol 33 (7) ◽

pp. 1957-1965

Author(s):

Yiliang Li ◽

Jinjin Li ◽

Jun-e Feng ◽

Hongkun Wang

Keyword(s):

Topological Space ◽

Topological Spaces ◽

Sufficient Condition ◽

General Topological Space ◽

Minimal Base ◽

This paper investigates minimal bases and minimal sub-bases for topological spaces. First, a necessary and sufficient condition is derived for the existence of minimal base for a general topological space. Then the concept of minimal sub-base for a topological space is proposed and its properties are discussed. Finally, for Alexandroff spaces, some special results with respect to minimal bases and minimal sub-bases are illustrated.

Existence of blowup solutions for nonlinear problems with a gradient term

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms/2006/80605 ◽

2006 ◽

Vol 2006 ◽

pp. 1-11 ◽

Cited By ~ 6

Author(s):

Faten Toumi

Keyword(s):

Continuous Function ◽

Positive Solution ◽

Nonlinear Problems ◽

Gradient Term ◽

Sufficient Condition ◽

Whole Space ◽

We prove the existence of positive explosive solutions for the equationΔu+λ(|x|)|∇u(x)|=ϕ(x,u(x))in the whole spaceℝN(N≥3), whereλ:[0,∞)→[0,∞)is a continuous function andϕ:ℝN×[0,∞)→[0,∞)is required to satisfy some hypotheses detailed below. More precisely, we will give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.