Approximate inverse systems which admit meshes

Mardešić, Sibe; Uglešić, Nikica

doi:10.1016/0166-8641(94)90093-0

Topology and its Applications

1994

DOI: 10.1016/0166-8641(94)90093-0

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Approximate inverse systems which admit meshes

Sibe Mardešić

Nikica Uglešić

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1995

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Numerical meshes and covering meshes of approximate inverse systems of compacta

Watanabe¹

1995

Proc. Amer. Math. Soc.

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Abstract. Mardesic and Rubin (1989) introduced approximate inverse systems of metric compacta by the conditions (A1)*-(A3)*. Mardesic and Watanabe (1988) introduced approximate inverse systems of topological spaces by the conditions (A1)-(A3). In this note we show that any approximate inverse system of metric compacta satisfies (A1)-(A3) if and only if it satisfies (A1)*-(A3)* for some matrices (see Theorem 1).S. Mardesic and L. Rubin [ 1 ] introduced the notion of approximate inverse system AA = {(Xa, da), £a,Paa>» A} of metric compacta. Hence, (A, <) is a directed preordered infinite set. (Xa, da) is a compactum endowed with a metric da , and paa< '■ Xa> -* Xa is a mapping defined whenever a < a' and is such that paa is the identity mapping. The real numbers ea > 0, a e A, are called numerical meshes. We require the following conditions:(Al)* (Va2 >aX> a)da(PaalPala1 , Paa2) < Sa ■ (A2)* (Va e A)(\jn > 0)(3a' > a)(\/a2 > a. > a')da(paaipaia2, paaf) < r¡.

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Numerical meshes and covering meshes of approximate inverse systems of compacta

Watanabe¹

1995

Proc. Amer. Math. Soc.

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show abstract

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Approximate inverse systems which admit meshes

Cited by 1 publication

References 10 publications

Numerical meshes and covering meshes of approximate inverse systems of compacta

Numerical meshes and covering meshes of approximate inverse systems of compacta

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