SOME CARDINAL PROPERTIES OF THE NEMYTSKY PLANE
Keywords:
topological space; Nemytsky plane; tightness, network weight, pseudocharacter, spread, extent, local dense, functional and weak tightness, preshannumber, -character, Shannumber.Abstract
. this article investigates the cardinal and topological properties of the Nemytsky plane. It is known that this plane is a separable space without a countable base, so it is not a metrizable space. This plane satisfies the first axiom of countability, and does not satisfy the second axiom of countability. We present some other interesting properties of the Nemytsky plane. The following cardinal invariants of the Nemytsky plane are found this paper: tightness, network weight, pseudocharacter, spread, extent, local dense, functional and weak tightness, preshannumber, - character, Shannumber, number of open sets. Other proofs are given about the Nemytsky plane is not normal space, about the uncountability of the weight, and about the countability of the character of the Nemytsky plane.
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