In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

Suppose that X is an infinite set with |X| ≥ q ≥ א0 and I X is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA using certain subsets A of X of the Baer-Levi semigroup BL q {α ∈ I X : dom α X and |X \ Xα| q}. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of BL q , but these are far more...

In 1937, Baer [5] introduced the notion of the type of an element in a torsion-free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion-free abelian groups of rank 1. Since then, despite the efforts of such mathematicians as Kurosh [23] and Malcev [25], no satisfactory system of complete invariants has been found for the torsion-fre...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

The adduct formation of 2′-deoxyguanosine (dG) with L-adrenaline under biomimetic conditions (pH 7.5, 37°C) with or without oxidant (MnO2) was demonstrated in order to clarify the reaction mechanism and the structure. At least two adducts have been observed by liquid chromatography-electrospray ionization-ion trap mass spectrometry (LC-ESI-ion trap MS) and LC-photodiode array detection (LC-PAD)...

[1] Th deficit and excess were examined in the upper 500 m of the Southern Ocean from Sub-Antarctic to Seasonal Ice Zones (Australian sector) during austral spring 2001. Th fluxes at 100 m indicate that particle export was low in the North (46.9–51.0 S), minimal in the Polar and Inter-Polar Frontal Zones and high in the South ( 61 S). These results are in tight agreement with new production est...

A DO model (here also referred to a Paris model) is a model M of set theory all of whose ordinals are first order definable in M. Jeffrey Paris (1973) initiated the study of DO models and showed that (1) every consistent extension T of ZF has a DO model, and (2) for complete extensions T, T has a unique DO model up to isomorphism iff T proves V = OD. Here we provide a comprehensive treatment of...

We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that \almost every continuous real-valued function deened on 0,1] is nowhere diierentiable". As with the results of Banach and Mazurkiewicz, it appears...

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme, and its strengthening REF(L) (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here L is a language with a distinguished linear order <, and REF(L) consists of the universal closure of formulas of the form ∃x∀y1 < x · · · ∀yn < x φ(y1, · · ·...

Eilenberg and Mac Lane [1] explained the notion of a 'natural' embedding by giving a categorical definition. Starting from their examples, we argue that one could equally well explain natural as meaning 'uniformly definable in set theory'. But do the categorically natural embeddings coincide with the uniformly definable ones? This is partly a technical question about whether certain well-known ...