ON QUASI *-BARRELLED SPACES

Authors

  • S. G. GAYAL Arts, Science, Commerce College, Rahuri, RAHURI-413 705, (MAHARASHTRA), INDIA.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4680

Keywords:

quasi ∗-barrelled spaces, bornivorous ∗-barrel

Abstract

In this paper, a new class of .ocally convex spaces, called quasi *- barrelled spaces is introduced. These spaces are characterized by : A locally convex space $E$ is Quasi *-barrelled if every bornivorous *-barrel in $E$ is a neighbourhood of $O$ in $E$. This class of spaces is a generalization of quasi-barrelled spaces and *-barrelled spaces (K.Anjaneyulu; Gayal : Jour. Math. Phy. Sci. Madras, 1984). Some properties of quasi *-barrelled spaces are sturued. Lastly one example each of

(i) a quasi *-barrelled space which is not quasi-barrelled.

(ii) a quasi *-barrelled space which is not *-barrelled.

is given.

References

Anjaneyulu K. and Gayal S.G., "On *-barrelled Spaces", Jour. Math. Phy. Sci. Madras 18(2) (1984), 111-117.

Horvath, J., The topological vector spaces and distributions Vol-I, Addison Wesley publishing Co. (1966).

lyahen, S.O., "Some remarks on countably quasi-barrelled space-Proc" Edinburgh Math. Soc (2) 15 (1966/67), 29.'>-296.

Kelly J.L. and I. Namika, Linear Topological Spaces-Ven Non stand, New York (1963).

Krishna Murthy, V, "Conjugate locally convex Spaces", Math. Zeitschr. 87(1965), 334-344.

M. dewilde & C. Houet, "On increasing sequence of absolutely convex sets in locally convex spaces", Math. Ann. 192 (1971), 257-261.

Webb J. H., "Sequential convergence in locally convex space", Proc. Carnb. Phil. 64(1968) 341-364.

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Published

1990-12-01

How to Cite

GAYAL, S. G. (1990). ON QUASI *-BARRELLED SPACES. Tamkang Journal of Mathematics, 21(4), 341–344. https://doi.org/10.5556/j.tkjm.21.1990.4680

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Section

Papers