A topological space X is said to be S-closed if and only if for every semi-open cover of X there exists a finite subfamily such that the union of their closures cover X. For a Hausdorff space, the concept of S-closed is shown to be equivalent to the concept of extremally disconnected and nearly compact. Further it has been shown that EDH-closed spaces are precisely S-closed Hausdorff spaces.
The health and nutritional status of 839 rural school boys in the age group 5 to 17 years are reported. Their poor health and nutritional status warrants an improvement in the socio-economic status and level of education, and a well planned school health service programme according to the local needs.
Let (X,τ) be a completely Hausdorff space. LetP be any topological property which is implied by complete regularity. Let (X,τ), be minimal-P. Then it has been shown that (X,τ), is completely regular and hence compact.
has introduced a new class of topological spaces called E r spaces.This class generalizes the class of Hausdorff spaces.A space is said to be an E r space if every point is the intersection of a countable number of closed neighbourhoods.It is easy to see that a continuous function from a countably compact space into an E { -space is closed, since countable compactness is a weakly hereditary property preserved under continuous maps and a countablycompact subset of an E l -space is closed [1].In the present note we consider a class of spaces called functionally countably compact.A space is said to be functionally countably compact if whenever Hi is a countable open filterbase on X such that the intersection A of the elements of Hi is equal to the intersection of the closures of the elements of Hi, then Hi is a base for the neighbourhoods of A. Functionally countably compact E r spaces are characterized by the property: Every continuous function defined on them into an Erspace is closed.Another class of spaces called countably C-compact has been considered.A space (X, D) is countably C-compact if every countable C7-open cover of every closed subset has a finite subfamily, the closures of whose members cover the set.The following relationship exists: countably-compact => countably C-compact =* functionally countably compact.Also functionally countably compact + E x ^minimal E x .That these implications are not reversible is shown by the following examples.EXAMPLE 1.1.A countably C-compact space need not be countably compact.Let Z represent the set of positive integers, let Y denote the subset of the plane consisting of all points of the form (1/n, 1/m) and the points of the form (1/n, 0) for n and m in Z.Let X= YU {<» }.Topologize X as follows: Let each point of the form (1/n, 1/m) be open.Partition Z into infinitely many infinite equivalence classes, {Z i } ao i=i .Let a neighbourhood system for the point (1/i,0) be composed of all sets of the form G U F U {1/i, 0} with G= {(l/i,l/m)|m^&}
Selected anthropometric measurements of 500 rural school children are reported and compared with national and American standards. Their poor nutritional status warrants an improvement in the socio-economic status and literacy of the masses and a well planned school health service programme.