Numerical meshes and covering meshes of approximate inverse systems of compacta

Watanabe, Tadashi

doi:10.1090/s0002-9939-1995-1254858-5

Proc. Amer. Math. Soc.

1995

DOI: 10.1090/s0002-9939-1995-1254858-5

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Numerical meshes and covering meshes of approximate inverse systems of compacta

Tadashi Watanabe¹

Abstract: 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… Show more

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Cited by 2 publications

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Synthesis and antiherpetic activity of N-(3-amino-1-adamantyl)calix[4]arenes

Motornaya

Shokova

et al. 2006

Pharm Chem J

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p-(3-Amino-1-adamantyl)calix [4]arenes with free and alkylated lower rim, representing conjugates of the aminoadamantane pharmacophore fragment and the calixarene platform, were synthesized for the first time by the Curtius rearrangement route starting from p-(3-carboxy-1-adamantyl)calix [4]arenes. The synthesized compounds were evaluated for activity against herpes simplex virus 2 (HSV-2). The nonalkylated compound with free phenol hydroxy groups is the first aminoadamantylcalixarene reported to possess antiviral properties (chemotherapeutic safety index, SI » 12.5). Alkylation at the lower rim of the calixarene platform leads to an increase in cytotoxicity and to the disappearance of anti-HSV activity.Calix[4]arenes (I) represent cyclic metacyclophanes, which are composed of phenol fragments bridged by methylene groups. These compounds have recently received much attention for their ability to serve as receptors of metal ions and neutral molecules, which opens up ways to using them as carriers, sensors, chromatographic media, ligands in homogeneous catalysis, etc.[1].Although the antituberculous activity of p-tert-octylcalix[8]arene modified at the lower rim with poly(oxyethylene) substituents (I with R = tert-octyl, X = (CH 2 CH 2 O) n H, n = 8) was observed as long ago as in 1955 (then it was considered a tetramer) [2 -4], data available on the pharmacological properties of calixarene derivatives are still rather restricted. In 1996, Casnati et al. reported on the antimicrobial activity of vancomycin antibiotic mimetics based on calix[4]arenes modified with dipeptide bridges at the upper rim [5]. Various calixarene derivatives with sulfonate, carboxylate, phosphoryl, and sulfamide groups at the upper rim were patented as antithrombotic [6], antiviral [7 -9], antimicrobial [10], and antibacterial, antifungal, and antitumor [11] agents. Among calix[n]arenes (n = 4, 6, 8), derivatives with R = SO 3 Na, (CH 2 ) m CO 2 H (m = 0 -2), PO 3

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Synthesis and antiherpetic activity of N-(3-amino-1-adamantyl)calix[4]arenes

Motornaya

Shokova

et al. 2006

Pharm Chem J

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Cohomological dimension and approximate limits

Rubin

1997

Proc. Amer. Math. Soc.

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Abstract. Approximate (inverse) systems of compacta have been useful in the study of covering dimension, dim, and cohomological dimension over an abelian group G, dim G . Such systems are more general than (classical) inverse systems. They have limits and structurally have similar properties. In particular, the limit of an approximate system of compacta satisfies the important property of being an approximate resolution. We shall prove herein that if G is an abelian group, a compactum X is the limit of an approximate system of compacta Xa, n ∈ N, and dim G Xa ≤ n for each a, then dim G X ≤ n.

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Numerical meshes and covering meshes of approximate inverse systems of compacta

Cited by 2 publications

References 11 publications

Synthesis and antiherpetic activity of N-(3-amino-1-adamantyl)calix[4]arenes

Synthesis and antiherpetic activity of N-(3-amino-1-adamantyl)calix[4]arenes

Cohomological dimension and approximate limits

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