This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (in Lukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

 

New classes of sets called Ω-open sets and Ωs-open sets are introduced and studied. Also, as applications we introduce and study Ω-compact spaces and Ωs- compact spaces.

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies introduced by Ying. The concepts of fuzzifying regular derived set, fuzzifying regular interior, and fuzzifying regular convergence are studied and some results on above concepts are obtained. Also, the concepts of fuzzifying completely continuous functions and fuzzifying R-map are introduced and some
important characterizations are obtained. Furthermore, some compositions of fuzzifying continuity with fuzzifying completely continuous functions and fuzzifying R-map are presented.
© 2006 Elsevier B.V.

 

In this paper, the concepts of pre-irresolute functions and strong compactness in the framework of fuzzifying topology were characterized in terms of pre-open sets. Some properties of fuzzifying pre-irresolute functions and fuzzifying strong compactness are discussed.

 

In this paper the concepts of fuzzifying γ −irresolute functions and fuzzifying γ -compact spaces are characterized in terms of fuzzifying γ -open sets and some of their properties are discussed.

© 2006 International Fuzzy Mathematics Institute-Los Angeles
 

The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets, η-continuity and ηζ-continuity and to obtain a decomposition of continuity.

@ 2006 Akade´miai Kiado´, Budapest.

In this paper, we introduce and study T0γ-,  R0γ-,  T1γ-, R1γ; T2γ- , T3γ-, T4γ-, strong T3γ- and strong T4γ-  separation axioms in fuzzifying topology and
give some of their characterizations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen, Fuzzy Sets and Systems, 57 (1993), 111-123.

© 2006 International Fuzzy Mathematics Institute-Los Angeles

Geologic investigation on the basement rocks exposed around Wadi Shait revealed that they constitute part of a fold thrust nappes comprising Gardan ophiolitic mélange structural unit (GOM) exposed in a tectonic contact against the Shait granite complex (SGC). Both units are brittly to ductily deformed, and are partially intruded by the calc-alkaline Hamash granodiorite, Dokhan volcanics, post-orogenic alkali granite and the Natash volcanics. Litholgically, the GOM builds up a stack of sliced sequence comprising low-grade regionally metamorphosed epiclastic, volcanogenic pyroclastic, basic and intermediate lava flows and structurally topped by metagabbro and hornblende metagabbro slices. On the other hand, the SGC is composed mainly of mesocratic tonalite, minor leucocratic trondhjemite, granodiorite and monzogranite. The latter occurs as dyke-like masses intruding the outcrops of the other rock varieties. This lithologic association denotes that the SGC constitutes a widely evolved complex in which the early members are deep-seated, calc-alkaline and I-type whereas the later members are shallower and clearly intrusive. Field data revealed that the stacking nature and consequently uplifting of the SGC were related to late orogenic extension associated with shortening phases controlled by Najd transformed faults. Detailed field mapping and petrographic studies carried out on the Wadi Shait area show evidence of polyphase deformation (D1-D4) affecting the SGC in addition to three metamorphic events (M1,M2 and M3) affecting the GOM.

The Shaitian granite complex (SGC) spans more than 80 Ma of crustal growth in the Arabian–Nubian Shield in southeast Egypt. It is a voluminous composite intrusion (60 km²) comprising a host tonalite massif intruded by subordinate dyke-like masses of trondhjemite, granodiorite and monzogranite. The host tonalite, in turn, encloses several, fine-grained amphibolite enclaves. U-Pb zircon dating indicates a wide range of crystallization ages within the SGC (800 ± 18 Ma for tonalites; 754 ± 3.9 Ma for trondhjemite; 738 ± 3.8 Ma for granodiorite; and 717 ± 3.2 Ma for monzogranite), suggesting crystallization of independent magma pulses. The high positive ε_Ndi (+6–+8) indicate that the melting sources were dominated by juvenile material without any significant input from older crust. Application of zircon saturation geothermometry indicates increasing temperatures during the generation of melts from 745 ± 31 °C for tonalite to 810 ± 25 °C for trondhjemite; 840 ± 10 °C for granodiorite; and 868 ± 10 °C for monzogranite. The pressure of partial melting is loosely constrained to be below the stability of residual garnet (<10 kbar) as inferred from the almost flat HREE pattern ((Gd/Lu)_N = 0.9–1.1), but >3 kbar for the stability of residual amphibole as inferred from the significantly lower Nb_N and Ta_N compared with LREE_N and the sub-chondrite Nb/Ta ratios exhibited by the granitic phases. The inverse relation between the generation temperatures and the ages estimates of the granitoid lithologies argue against a significant role of fractional crystallization. The major and trace element contents indicate the emplacement of the SGC within a subduction zone setting. It lacks distinctive features for melt derived from a subducted slab (e.g. high Sr/Y and high (La/Yb)_N ratios), and the relatively low MgO and Ni contents in all granite phases within the SGC suggest melting within the lower crust of an island arc overlying a mantle wedge. Comparison with melts produced during melting experiments indicates an amphibolite of basaltic composition is the best candidate as source for the tonalite, trondhjemite and granodiorite magmas whereas the monzogranite magma is most consistent with fusion of a tonalite protolith. Given the overlapping Sm-Nd isotope ratios as well as several trace element ratios between monzogranite and tonalite samples, it is reasonable to suggest that the renewed basaltic underplating may have caused partial melting of tonalite and the emplacement of monzogranite melt within the SGC. The emplacement of potassic granite (monzogranite) melts subsequent to the emplacement of Na-rich granites (tonalite-trondhjemite-granodiorite) most likely suggests major crustal thickening prior arc collision and amalgamation into the over thickened proto-crust of the Arabian-Nubian shield. Eventually, after complete consolidation, the whole SGC was subjected to regional deformation, most probably during accretion to the Saharan Metacraton (arc–continent collisions) in the late Cryogenian -Ediacaran times (650–542 Ma).

Geologic investigation on the basement rocks exposed around Wadi Shait revealed that they constitute part of a fold thrust nappes comprising Gardan ophiolitic mélange structural unit (GOM) exposed in a tectonic contact against the Shait granite complex (SGC). Both units are brittly to ductily deformed, and are partially intruded by the calc-alkaline Hamash granodiorite, Dokhan volcanics, post-orogenic alkali granite and the Natash volcanics. Litholgically, the GOM builds up a stack of sliced sequence comprising low-grade regionally metamorphosed epiclastic, volcanogenic pyroclastic, basic and intermediate lava flows and structurally topped by metagabbro and hornblende metagabbro slices. On the other hand, the SGC is composed mainly of mesocratic tonalite, minor leucocratic trondhjemite, granodiorite and monzogranite. The latter occurs as dyke-like masses intruding the outcrops of the other rock varieties. This lithologic association denotes that the SGC constitutes a widely evolved complex in which the early members are deep-seated, calc-alkaline and I-type whereas the later members are shallower and clearly intrusive. Field data revealed that the stacking nature and consequently uplifting of the SGC were related to late orogenic extension associated with shortening phases controlled by Najd transformed faults. Detailed field mapping and petrographic studies carried out on the Wadi Shait area show evidence of polyphase deformation (D1-D4) affecting the SGC in addition to three metamorphic events (M1,M2 and M3) affecting the GOM.