# A topological view of P-spaces

@article{Misra1972ATV, title={A topological view of P-spaces}, author={A. K. Misra}, journal={General Topology and Its Applications}, year={1972}, volume={2}, pages={349-362} }

Abstract A T 1 space in which the intersection or any countably many open sets is open, is called a P-space. In the present paper some basic topological properties of these spaces are studied. Three main results are a characterization of regular paracompact P-spaces, a product theorem for realcompact P-spaces and an example of a Hausdorff connected P-space.

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#### References

SHOWING 1-10 OF 15 REFERENCES

A note on paracompact spaces

- Mathematics
- 1953

Let us quickly recall the definitions of the terms which are used in the statement of Theorem 1, and which will be used throughout this paper. Let X be a topological space. A collection <R of subsets… Expand

Concerning rings of continuous functions

- Mathematics
- 1954

The present paper deals with two distinct, though related, questions, concerning the ring C(X, R) of all continuous real-valued functions on a completely regular topological space X. The first of… Expand

A theory of transfinite convergence

- Mathematics
- 1949

The classical theory of convergence, resting as it does on the properties of the real numbers, is intimately connected with the notion of denumerability. As examples of what is meant we recall that a… Expand

A class of function algebras

- Mathematics
- 1960

Introduction. A problem which has generated considerable interest during the past couple of decades is that of characterizing abstractly systems of realvalued continuous functions with various… Expand