Structures with isothermal cores have been discussed in great detail in the literature, but for all these structures the value of dP/d rho jumps at the core-envelope boundary. The authors have chosen cores with extreme relativistic conditions (dP/d rho =1 and 1/3). For such cores one can ensure the continuity of dP/d rho along with that of pressure, density, elambda and enu . Choosing polytropic envelopes, which have positive distribution function for all possible energies provided that dP/d rho <or=1, the central redshifts have been calculated. One can obtain any high value of central redshift. The structures are pulsationally stable for Zc<or=1.43 when the polytropic index n=1. For n<1, one may obtain a maximum central redshift of 4.75 for pulsationally stable structures. Next, an envelope in which the density is a specific function of r is chosen. By assuming the surface density to be equal to 2*1014 g cm-3, the mass of neutron stars has been calculated. The maximum mass of 4.7 M(.) is consistent with the results of other authors.