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In this paper we give some significative counterexamples to prove that some well known generalizations of Lindelof property are proper Also we give some new results, we introduce and study the almost regular-Lindelof spaces as a generalization of the almost-Lindel0f spaces and as a new and significative application of the quasi-regular open subsets of ].
We consider the integral equation h(u(t)) = f R I g(t, x)u(x) dx , with t ∈ [0, 1], and prove an existence theorem for bounded solutions where f is not assumed to be continuous.
We deal with the integral equation u(t) = f( R I g(t, z)u(z) dz), with t ∈ I = [0, 1], f : R → R and g : I×I → [0,+∞[. We prove an existence theorem for solutions u ∈ L(I,R) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1.
In this paper, we define and investigate the continuous retraction and the -continuous fixed point property. Theorem of Connell 11] and Theorem 3.4 of Arya and Deb  are improved.
Some results on cleavability theory are presented. We also show some new ’s results.
Article history: Received 28 April 2014 Received in revised form 14 October 2014 Accepted 14 October 2014 Available online 31 October 2014 MSC: 54D20