A topological space X is called C-normal if there exist a normal space Y and a bijective functionis a homeomorphism for each compact subspace C ⊆ X. We investigate this property and present some examples to illustrate the relationships between C-normality and other weaker kinds of normality.

A topological space ( X , τ ) is called epinormal if there is a coarser topology τ on X such that ( X , τ ) is T 4 . We investigate this property and present some examples to illustrate the relationships between epinormality and other weaker kinds of normality.

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A topological space X is called C-Tychonoff if there exist a one-to-one function f from X onto a Tychonoff space Y such that f restriction K from K onto f(K) is a homeomorphism for each compact subspace K of X. We discuss this property and illustrate the relationships between C-Tychonoffness and some other properties like submetrizability, local compactness, L-Tychononess, C-normality, C-regularity, epinormality, sigma-compactness, pseudocompactness and zero-dimensional.

In this paper, the flow of hybrid nanofluids in a three-dimensional rectangular channel consisting of three perpendicular blocks will be analyzed in terms of heat transfer. The two perpendicular rectangular blocks are rotating with speed ω . The hybrid mixture consists of aluminum oxide and copper, and each of them will contain in volume fraction of 0.001 to 0.25. The κ - ε model of turbulent flow along with Navier and energy equation will be brought into action by using the finite element package COMSOL Multiphysics 5.6. Volume fraction and speed of rotation will be used as the parameters, and a parameter study will be done by fixing the Reynolds number Re = 50,000 with energy dissipation rate ( ε ) ( m 2 / s 3 ) ( 3.46 E − 6 to 3.76 E − 5 ), kinetic energy ( κ ) ( m 2 / s 2 ) ( 2.50 E − 06 to 1.23 E − 05 ), and the Prandtl number (0.98506 to 1.2625). It was deducted that the local Nusselt number is minimized at the outlet for stationary blocks and the maximum for the moving blocks. In addition, the mean number of Nusselt on the upper surface of the rectangular channel increases when the blocks are stationary and decreases when the blocks are moving. The study suggests that to maximize the conduction process in the channel the blocks must rotate with a certain velocity. This study also determined that with increasing the total viscosity of hybrid nanofluids, the average temperature is decreasing linearly in the middle of the channel whether the blocks are rotating or not. The temperature gradient along the z -axis decreases with increasing volume fraction only when blocks are stationary. In addition, it has been determined that the maximum average temperature occurs when the volume fractions of copper and oxide are equal to 0.001.