Faintly continuous (FC) functions, entitled faintly S-continuous and faintly δS-continuous functions have been introduced and investigated via a -open and -open sets. Several characterizations and properties of faintly S-continuous and faintly -Continuous functions were obtained. In addition, relationships between faintly s- Continuous and faintly S-continuous function and other forms of FC function were investigated. Also, it is shown that every faintly  S-continuous is weakly S-continuous. The Convers is shown to be satisfied only if the co-domain of the function is almost regular.

High temperature superconductors with a nominal composition HgBa2Ca2Cu3O8+δ
for different values of pressure (0.2,0.3, 0.5, 0.6, 0.9, 1.0 & 1.1)GPa were prepared by
a solid state reaction method. It has been found that the samples were semiconductor
P=0.2GPa.while the behavior of the other samples are superconductor in the rang
(80-300) K. Also the transition temperature Tc=143K is the maximum at P is equal to
0.5GPa. X-ray diffraction showed a tetragonal structure with the decreasing of the
lattice constant c with the increasing of the pressure. Also we found an increasing of
the density with the pressure.

The influences of the Cu substitution at Hg site in the HgOd layer, upon the
microstructure, Tc and oxygen content of Hg-1223 have been investigated. High
temperature superconductor with a nominal composition Hg1-xCuxBa2Ca2Cu3O8 + δ for
Cu ( 0 £ x £ 0.5) have been prepared by the two-steps solid state reaction method
under optimum conditions. XRD showed a tetragonal structure with a high ratio of
Hg-1223 superconductor phase. Tc enhancement has been determined with the Cu
concentration was is found to be Tc = 153 K for x = 0.3, while the oxygen content
observed variously with Cu concentration. Hg1-xCuxBa2Ca2Cu3O8+δ structure, oxygen
content and Tc behavior have been discussed.