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This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

On a class of continuous mappings

Karol Borsuk, R. Molski (1958)

Fundamenta Mathematicae

On a Class of Darboux Functions from a Topological Space to a Uniform Space

Beloslav Riečan (1971)

Matematický časopis

On a class of multi-valued vector fields in Banach spaces

J. Bryszewski (1977)

Fundamenta Mathematicae

On a class of subalgebras of C(X) with applications to βX

Donald Plank (1969)

Fundamenta Mathematicae

On a classification of pointwise compact sets of the first Baire class functions

Witold Marciszewski (1989)

Fundamenta Mathematicae

On a concept of dependence for continuous mappings

Karol Borsuk (1956)

Fundamenta Mathematicae

On a family of 2-dimensional AR-sets

Karol Borsuk (1962)

Fundamenta Mathematicae

On a generalization of absolute neighborhood retracts

Michael Clapp (1971)

Fundamenta Mathematicae

On a generalization of Dugundji extension theorem

W. Kulpa (1976)

Colloquium Mathematicae

On $a$ -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If $X$ is a Tychonoff space, $C (X)$ its ring of real-valued continuous functions. In this paper, we study non-essential ideals in $C (X)$ . Let $a$ be a infinite cardinal, then $X$ is called $a$ -Kasch (resp. $\bar{a}$ -Kasch) space if given any ideal (resp. $z$ -ideal) $I$ with $gen (I) < a$ then $I$ is a non-essential ideal. We show that $X$ is an $ℵ_{0}$ -Kasch space if and only if $X$ is an almost $P$ -space and $X$ is an $ℵ_{1}$ -Kasch space if and only if $X$ is a pseudocompact and almost $P$ -space. Let $C_{F} (X)$ denote the socle of $C (X)$ . For a topological space $X$ with only...

On a method of constructing ANR-sets. An application of inverse limits

J. Krasinkiewicz (1976)

Fundamenta Mathematicae

On a mixed-type interpolation problem for real polynomials

Zalman Rubinstein (1984)

Annales Polonici Mathematici

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