The purpose of this paper is to show that every almost periodic homeomorphism of the 2-sphere or the annulus onto itself is topologically equivalent to either a standard rotation or a standard reflection or the composition of a standard reflection with a standard rotation of these spaces.
A new property of pseudo-open functions is presented in this paper. Pseudo-open functions are monotonic decreasing with respect to ordinal and cardinal invariants defined by compact and sequential closures. A weak form of continuity, called k-continuous, is defined, characterized and used in the proof of the monotonicity properties of pseudo-open mappings. The relationships between the classes of k-continuous and sequentially continuous mappings in the category of all topological spaces and the continuous mappings in the subcategories of k-spaces and sequential spaces are presented.
In this paper we answer questions of Arhangel'skii and Michael by providing an example of a regular symmetrizable space which is not subparacompact and has a closed subset which is not a Gσ-set. We also use the idea of sequential order to obtain some positive results, and several examples are provided which show that these results are in some sense the best possible.
Arhangel'skiǐ proved that the Continuum Hypothesis implies that if a regular space X is hereditarily of pointwise countable type then the set of points as which the character of X is countable is a dense subset of X. In this note we prove this theorem without the use of the Continuum Hypothesis.
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