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...

The set of all transformation monoids on a fixed set of infinite cardinality λ, equipped with the order of inclusion, forms a complete algebraic lattice Mon(λ) with 2 compact elements. We show that this lattice is universal with respect to closed sublattices, i.e., the closed sublattices of Mon(λ) are, up to isomorphism, precisely the complete algebraic lattices with at most 2 compact elements....

Assuming w is the only measurable cardinal, we prove: (i) Let ~ be an equivalence relation such that ~ = =z. for some logic L < L* satisfying Robinson's consistency theorem (with L* arbitrary); then there exists a strongest logic L+ « L* such that ~ = =/.+ ; in addition, L+ is countably compact if ~^= . (ii) Let ~ be an equivalence relation such that ~ = =/." for some logic L° satisfying Robins...

In this paper, we introduce and study new concepts of order L-weakly M-weakly compact operators. As consequences, obtain some characterizations Banach lattices with continuous norms or whose topological duals have norms. It is proved that if $$T:E \longrightarrow F$$ an operator between two lattices, then T only its adjoint $$T'$$ compact. Also, show compact, Some related results are also obtai...

We show that the space Lip0(R) is the dual space of L(R;R)/N where N is the subspace of L(R;R) consisting of vector fields whose divergence vanishes identically. We prove that although the quotient space L(R;R)/N is weakly sequentially complete, the subspace N is not nicely placed in other words, its unit ball is not closed for the topology τm of local convergence in measure. We prove that if Ω...

Pot marigold (Calendula officinalis L.) is a medicinal and ornamental plant. The effect of different concentrations of chlormequat (cycocel), and daminozide, two plant growth retardant, on plant height, flowering, the content of essence and some other traits in pot marigold (Calendula officinalis) was assessed. Plant growth retardants are commonly applied to limit stem elongation and produce a ...

where it is assumed that the “resolvent” L, = (T + (l/n)l)-i, II = 1, 2,... exists and is defined at least on the range of the operator f C. Such a class of operators T includes all m-accretive operators (cf. Kato ] 5 I). The equations (G,) can be solved by a degree theory argument if we assume, among other things, that L, is compact and C is continuous and bounded, or that L, is continuous and...

In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...