The Journal of the Indian Mathematical Society

K. Padmavally ¹

Affiliations
1 Ramanujan Institute of Mathematics, IN

Abstract

In this paper a boundary value problem conneoted with the study of neutron flux in a reactor is investigated. Consider an infinite reactor in which the plane segments y = 0, - 1 ≤ x ≤ 1, x = 0, - l ≤ y ≤ l are occupied by control rods (assumed to be of zero thickness).

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K. Padmavally ¹

Affiliations
1 Ramanujan Institute of Mathematics (Karaikudi), Madras, IN

Abstract

Theorem 1 of [2] states that the condition for every closed set A and any limit point p of A, there exists a subset Z of A not containing p but of which p is the sole complete limit point is necessary and sufficient for the space to be minimally bicompact. The proof ([2] page 2) of the sufficiency of this condition assumes that the closure of the set S under the new topology is A -p where A is its closure under the given topology and p some limit point of S (not belonging to S).

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K. Padmavally ¹

Affiliations
1 Ramanujan Institute of Mathematics (Karaikudi), Madras, IN

Abstract

C. T. Rajagopal [4] has proved the following two theorems deducing the second theorem from the first and presenting it as an integral analogue of a theorem of M. S. Macphail [3, Theorem I ].

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K. Padmavally ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

In this paper a necessary and sufficient condition for a space to be minimally bicompact is established. Also the question of the existence of a minimally bicompact topology weaker than a given bicompact topology is considered, and it is shown that the set P_t of points at which a (bicompact) topology t is minimally bicompact can be increased (by weakening it) by any scattered set.

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