It is the purpose of this paper to prove that if each of X and Y is a compact Hausdorff space containing infinitely many points, and X X Y is the continuous image of a compact ordered space L, then both X and Fare metrizable.2 The preceding theorem is a generalization of a theorem [l ] by Mardesic and Papic, who assume that X, Y, and L are also connected. Young, in [3], shows that the Cartesian...

A recent article in The Intelligencer described in some detail the theory of non-well-founded sets for the purpose of being able to solve freely equations of the sort X = A × X with A fixed ([Barwise & Moss, 1991]). Of course, the empty set is a solution, but what was wanted was a non-empty solution (in fact, the largest solution, if such exists). If X were a non-empty solution and x ∈ X, then ...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

Let E be a computably enumerable (c.e.) equivalence relation on the set ω of natural numbers. We say that the quotient set ω/E (or equivalently, the relation E) realizes a linearly ordered set L if there exists a c.e. relation E respecting E such that the induced structure (ω/E;E) is isomorphic to L. Thus, one can consider the class of all linearly ordered sets that are realized by ω/E; formall...

The notation "" for OR is bad and misleading. Just think that in the context of boolean functions, the author uses  instead of ∨.The integers modulo 2, that is Z2  0,1, have an addition where 1  1  0 while 1 ∨ 1  1. A set A is partially ordered by a binary relation ≤, if this relation is reflexive, that is a ≤ a holds for every element a ∈ S, it is transitive, that is if a ≤ b and b ≤ c...