Order-continuous functions and order-connected spaces

1970 ◽  
Vol 68 (1) ◽  
pp. 27-31 ◽  
Author(s):  
D. C. J. Burgess ◽  
S. D. McCartan
Keyword(s):  
Continuous Functions ◽  
Relative Importance ◽  
Connected Space ◽  
Order Continuity ◽  
Ordered Space ◽  
Order Continuous ◽  
Connected Spaces

We introduce and compare four procedures for defining the order-continuity of a function from one topological ordered space into another, where each reduces to the usual conception when the orderings of the two spaces are trivial. Chiefly for the purposes of this comparison, we use the idea of an ‘order-connected’ space, and in the course of investigating under which types of order-continuous functions this property is preserved, we are helped in assessing their relative importance.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Order continuous measures

1964 ◽  
Vol 60 (2) ◽  
pp. 205-207 ◽  
Author(s):  
G. T. Roberts
Keyword(s):  
Topological Space ◽  
Linear Form ◽  
Vector Lattice ◽  
Measure Zero ◽  
Continuous Functions ◽  
Order Convergence ◽  
Locally Compact ◽  
Compact Topological Space ◽  
Continuous Measures ◽  
Order Continuous

1. Objective. It is possible to define order convergence on the vector lattice of all continuous functions of compact support on a locally compact topological space. Every measure is a linear form on this vector lattice. The object of this paper is to prove that a measure is such that every set of the first category of Baire has measure zero if and only if the measure is a linear form which is continuous in the order convergence.

scholarly journals New types of locally connected spaces via clopen set

2021 ◽  
Vol 40 (3) ◽  
pp. 671-679
Author(s):  
Ennis Rafael Rosas Rodríguez ◽  
Sarhad F. Namiq
Keyword(s):  
Connected Space ◽  
New Type ◽  
Connected Spaces

In this paper, we define and study a new type of connected spaces called λco-connected space. It is remarkable that the class of λ-connected spaces is a subclass of the class of λco-connected spaces. We discuss some characterizations and properties of λco-connected spaces, λco components and λco-locally connected spaces

The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II

1992 ◽  
Vol 122 (1-2) ◽  
pp. 127-135 ◽  
Author(s):  
John W. Rutter
Keyword(s):  
Group Extension ◽  
Equivalence Classes ◽  
Homotopy Groups ◽  
Geometric Proof ◽  
Homotopy Equivalence ◽  
Connected Space ◽  
Abelian Kernel ◽  
Simply Connected ◽  
Extension Sequence ◽  
Connected Spaces

SynopsisWe give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.

Riesz spaces with the order-continuity property. I

1977 ◽  
Vol 81 (1) ◽  
pp. 31-42 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Riesz Space ◽  
Continuity Property ◽  
Sequential Order ◽  
Order Continuity ◽  
Linear Map ◽  
Riesz Spaces ◽  
Quotient Spaces ◽  
Positive Linear Map ◽  
Order Continuous

A Riesz space E has the (sequential) order-continuity property if every positive linear map from E to an Archimedean Riesz space is (sequentially) order-continuous. This is the case if and only if the canonical maps from E to its Archimedean quotient spaces are all (sequentially) order-continuous. I relate these properties to others that have been described elsewhere.

Riesz spaces with the order-continuity property. II

1978 ◽  
Vol 83 (2) ◽  
pp. 211-223 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Internal Structure ◽  
Riesz Space ◽  
Continuity Property ◽  
Order Continuity ◽  
Linear Map ◽  
Riesz Spaces ◽  
Positive Linear Map ◽  
Order Continuous

I continue to investigate Riesz spaces E with the property that every positive linear map from E to an Archimedean Riesz space is sequentially order-continuous. In order to give a criterion for the product of such spaces to be another, we are forced to investigate their internal structure, and to develop an ordinal hierarchy of such spaces.

scholarly journals ON SEPARATE ORDER CONTINUITY OF ORTHOGONALLY ADDITIVE OPERATORS

2021 ◽  
Vol 9 (1) ◽  
pp. 200-209
Author(s):  
I. Krasikova ◽  
O. Fotiy ◽  
M. Pliev ◽  
M. Popov
Keyword(s):  
Order Continuity ◽  
Vector Lattices ◽  
Additive Operator ◽  
Uniformly Convergent ◽  
Orthogonally Additive Operator ◽  
Orthogonally Additive ◽  
Order Continuous ◽  
Orthogonally Additive Operators

Our main result asserts that, under some assumptions, the uniformly-to-order continuity of an order bounded orthogonally additive operator between vector lattices together with its horizontally-to-order continuity implies its order continuity (we say that a mapping f : E → F between vector lattices E and F is horizontally-to-order continuous provided f sends laterally increasing order convergent nets in E to order convergent nets in F, and f is uniformly-to-order continuous provided f sends uniformly convergent nets to order convergent nets).

scholarly journals Pythagorean Fuzzy Rough Connected Spaces

2021 ◽  
Vol 2070 (1) ◽  
pp. 012069
Author(s):  
P Revathi ◽  
R Radhamani
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
Connected Space ◽  
Fuzzy Rough Set ◽  
Connected Spaces

Abstract In this paper Pythagorean fuzzy rough set and Pythagorean fuzzy rough topological spaces are defined for the connected space. Then, the properties of connectedness are discussed with examples.

scholarly journals Almost locally connected spaces

1981 ◽  
Vol 31 (4) ◽  
pp. 421-428 ◽  
Author(s):  
Vincent J. Mancuso
Keyword(s):  
Connected Space ◽  
Local Connectedness ◽  
Quotient Maps ◽  
Regular Open ◽  
Connected Spaces ◽  
Open Maps

AbstractThis paper introduces the concept of an almost locally connected space. Every locally connected space is almost locally connected, and the concepts are equivalent in the class of semi-regular spaces. Almost local connectedness is hereditary for regular open subspaces, is preserved by continuous open maps, but not generally by quotient maps. It is productive in the presence of almost-regularity.

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