On a Question concerning Sharp Bases
نویسندگان
چکیده
A sharp base B is a base such that whenever (Bi)i<ω is an injective sequence from B with x ∈ i<ω Bi, then { ⋂ i<n Bi : n < ω} is a base at x. Alleche, Arhangel’skĭı and Calbrix asked: if X has a sharp base, must X × [0, 1] have a sharp base? Good, Knight and Mohamad claimed to construct an example of a Tychonoff space P with a sharp base such that P × [0, 1] does not have a sharp base. However, the space was not regular. We show how to modify the construction to make P Tychonoff.
منابع مشابه
Operator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کاملOn the Metrizability of Spaces with a Sharp Base
A base B for a space X is said to be sharp if, whenever x ∈ X and (Bn)n∈ω is a sequence of pairwise distinct elements of B each containing x, the collection { ⋂ j≤n Bj : n ∈ ω} is a local base at x. We answer questions raised by Alleche et al. and Arhangel’skĭı et al. by showing that a pseudocompact Tychonoff space with a sharp base need not be metrizable and that the product of a space with a ...
متن کاملBases Consisting of Rational Functions of Uniformly Bounded Degrees or More General Functions
We prove in this paper the existence of a Schauder basis for C[0, 1] consisting of rational functions of uniformly bounded degrees. This solves an open question of some years standing concerning the possible existence of such bases. This result follows from a more general construction of bases on R and [0, 1]. We prove that the new bases are unconditional bases for Lp , 1<p< , and Besov spaces....
متن کاملOn a Result of Tohge concerning the Unicity of Meromorphic Functions
In this paper we prove some uniqueness theorems of meromorphic functions which improve a result of Tohge and answer a question given by him. Furthermore, an example shows that the conditions of our results are sharp.
متن کاملA Step in Castelnuovo Theory via Gröbner Bases
We establish the first previously unknown case of the EisenbudHarris conjecture in Castelnuovo theory concerning algebraic curves of high genus in Pn. The problem is reduced to a question about zero-dimensional schemes Γ ⊂ P in symmetric position with certain constrains on the Hilbert function. The method of Gröbner bases is then applied to study the homogeneous ideal of Γ.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005