• Title/Summary/Keyword: m-Urysohn

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MINIMAL P-SPACES

  • Arya, S.P.;Bhamini, M.P.
    • Kyungpook Mathematical Journal
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    • v.27 no.1
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    • pp.27-33
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    • 1987

  • Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

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ON A SYSTEM OF NONLINEAR INTEGRAL EQUATION WITH HYSTERESIS

  • Darwish, M.A.
    • Journal of applied mathematics & informatics
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    • v.6 no.2
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    • pp.407-416
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    • 1999

  • In this paper we give some sufficient conditions for the existence and uniqueness of a continuous for the existence and uniqueness of a continuous slution of the system of Urysohn-Volterra equation with hysteresis.