Some results on the existence of utility functions on path connected spaces

1987 ◽  
Vol 16 (2) ◽  
pp. 147-156 ◽  
Author(s):  
Paulo Klinger Monteiro
Keyword(s):  
Utility Functions ◽  
Path Connected ◽  
Connected Spaces

scholarly journals Almost-continuous path connected spaces

1981 ◽  
Vol 4 (4) ◽  
pp. 823-825
Author(s):  
Larry L. Herrington ◽  
Paul E. Long
Keyword(s):  
Continuous Function ◽  
Connected Components ◽  
Continuous Path ◽  
Open Set ◽  
Regular Open ◽  
Path Connected ◽  
Almost Continuous ◽  
Connected Spaces

M. K. Singal and Asha Rani Singal have defined an almost-continuous functionf:X→Yto be one in which for eachx∈Xand each regular-open setVcontainingf(x), there exists an openUcontainingxsuch thatf(U)⊂V. A spaceYmay now be defined to be almost-continuous path connected if for eachy0,y1∈Ythere exists an almost-continuousf:I→Ysuch thatf(0)=y0andf(1)=y1An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components ofY.

Utility functions on locally connected spaces

2004 ◽  
Vol 40 (6) ◽  
pp. 701-711 ◽  
Author(s):  
Juan C Candeal ◽  
Esteban Induráin ◽  
Ghanshyam B Mehta
Keyword(s):  
Utility Functions ◽  
Connected Spaces

scholarly journals Finite, primitive and euclidean spaces

1988 ◽  
Vol 1 (3) ◽  
pp. 177-196 ◽  
Author(s):  
Efim Khalimsky
Keyword(s):  
Image Processing ◽  
Euclidean Space ◽  
Computer Tomography ◽  
Quotient Space ◽  
Robot Vision ◽  
Euclidean Spaces ◽  
Finite Spaces ◽  
Path Connected ◽  
Connected Spaces ◽  
Digital Spaces

Integer and digital spaces are playing a significant role in digital image processing, computer graphics, computer tomography, robot vision, and many other fields dealing with finitely or countable many objects. It is proven here that every finite T0-space is a quotient space of a subspace of some simplex, i.e. of some subspace of a Euclidean space. Thus finite and digital spaces can be considered as abstract simplicial structures of subspaces of Euclidean spaces. Primitive subspaces of finite, digital, and integer spaces are introduced. They prove to be useful in the investigation of connectedness structure, which can be represented as a poset, and also in consideration of the dimension of finite spaces. Essentially T0-spaces and finitely connected and primitively path connected spaces are discussed.

Preference orders and continuous representations

2011 ◽  
Vol 61 (1) ◽  
Author(s):  
Alessandro Caterino ◽  
Rita Ceppitelli ◽  
Ghanshyam Mehta
Keyword(s):  
Representation Theorem ◽  
Topological Spaces ◽  
Continuous Representation ◽  
Representation Theorems ◽  
Preference Orders ◽  
Separable Spaces ◽  
Path Connected ◽  
Continuous Representations ◽  
Connected Spaces

AbstractIn this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

scholarly journals Covering maps for locally path-connected spaces

2012 ◽  
Vol 218 (1) ◽  
pp. 13-46 ◽  
Author(s):  
N. Brodskiy ◽  
J. Dydak ◽  
B. Labuz ◽  
A. Mitra
Keyword(s):  
Path Connected ◽  
Connected Spaces

Connected Spaces and Path Connected Spaces

2020 ◽  
pp. 67-82
Author(s):  
Sasho Kalajdzievski ◽  
Derek Krepski ◽  
Damjan Kalajdzievski
Keyword(s):  
Path Connected ◽  
Connected Spaces

scholarly journals Returning functions with closed graph are continuous

2020 ◽  
Vol 70 (2) ◽  
pp. 297-304
Author(s):  
Taras Banakh ◽  
Małgorzata Filipczak ◽  
Julia Wódka
Keyword(s):  
Topological Space ◽  
Real Number ◽  
Positive Real Number ◽  
Connected Subset ◽  
Closed Graph ◽  
Positive Real ◽  
Contractible Spaces ◽  
Path Connected ◽  
Connected Spaces

Abstract A function f : X → ℝ defined on a topological space X is called returning if for any point x ∈ X there exists a positive real number Mx such that for every path-connected subset Cx ⊂ X containing the point x and any y ∈ Cx ∖ {x} there exists a point z ∈ Cx ∖ {x, y} such that |f(z)| ≤ max{Mx, |f(y)|}. A topological space X is called path-inductive if a subset U ⊂ X is open if and only if for any path γ : [0, 1] → X the preimage γ–1(U) is open in [0, 1]. The class of path-inductive spaces includes all first-countable locally path-connected spaces and all sequential locally contractible spaces. We prove that a function f : X → ℝ defined on a path-inductive space X is continuous if and only if it is returning and has closed graph. This implies that a (weakly) Świątkowski function f : ℝ → ℝ is continuous if and only if it has closed graph, which answers a problem of Maliszewski, inscribed to Lviv Scottish Book.

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