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1.
We present a method for describing all indecomposable subcontinua of . This method enables us to construct in a new subcontinuum of .
We also show that the nontrivial layers of standard subcontinua can be described by our method. This allows us to construct a layer with a proper dense -subset and bring the number of (known) nonhomeomorphic subcontinua of to 14.
2.
J. Hagler 《Proceedings of the American Mathematical Society》2002,130(11):3313-3324
Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .
3.
We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.
4.
The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of or .
5.
Louis Jeanjean Kazunaga Tanaka 《Proceedings of the American Mathematical Society》2003,131(8):2399-2408
We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in :
where . Without the assumption of the monotonicity of , we show that the mountain pass value gives the least energy level.
where . Without the assumption of the monotonicity of , we show that the mountain pass value gives the least energy level.