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Topology on ordered fields

Yoshio Tanaka — 2012

Commentationes Mathematicae Universitatis Carolinae

An ordered field is a field which has a linear order and the order topology by this order. For a subfield F of an ordered field, we give characterizations for F to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on F .

Tanaka spaces and products of sequential spaces

Yoshio Tanaka — 2007

Commentationes Mathematicae Universitatis Carolinae

We consider properties of Tanaka spaces (introduced in Mynard F., , Comment. Math. Univ. Carolin. (2002), 525–530), strongly sequential spaces, and weakly sequential spaces. Applications include product theorems for these types of spaces.

Products of k -spaces, and questions

Yoshio Tanaka — 2003

Commentationes Mathematicae Universitatis Carolinae

As is well-known, every product of a locally compact space with a k -space is a k -space. But, the product of a separable metric space with a k -space need not be a k -space. In this paper, we consider conditions for products to be k -spaces, and pose some related questions.

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