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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 Ê 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 (Ê I g(t, z) u(z) dz), with t ∈ I = [0, 1], f : R n → R n and g : I ×I → [0, +∞[. We prove an existence theorem for solutions u ∈ L ∞ (I, R n) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1.
Some results on cleavability theory are presented. We also show some new 's results. In 1985 Arhangel'skii in , , introduced various types of cleavability (originally called splittability) of topological spaces as follows. Let P be a class of topological spaces and M a class of continuous mappings (containing all homeomorphisms). Let A be a subset… (More)
a r t i c l e i n f o a b s t r a c t In this paper we are interested in monotone versions of partitionability of topological spaces and weak versions thereof. We identify several classes of spaces with these properties by constructing trees of open sets with various properties.