Displaying similar documents to “An answer to a question of Arhangel'skii”

On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces

Oleg Okunev (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if C p ( X ) is Lindelöf, Y = X ∪ { p } , and the point p has countable character in Y , then C p ( Y ) is Lindelöf; b) if Y is a cozero subspace of a Tychonoff space X , then l ( C p ( Y ) ω ) ≤ l ( C p ( X ) ω ) and ext ( C p ( Y ) ω ) ≤ ext ( C p ( X ) ω ) .

On embeddings into C p ( X ) where X is Lindelöf

Masami Sakai (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A.V. Arkhangel’skii asked that, is it true that every space Y of countable tightness is homeomorphic to a subspace (to a closed subspace) of C p ( X ) where X is Lindelöf? C p ( X ) denotes the space of all continuous real-valued functions on a space X with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace...

A remark on the tightness of products

Oleg Okunev (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We observe the existence of a σ -compact, separable topological group G and a countable topological group H such that the tightness of G is countable, but the tightness of G × H is equal to 𝔠 .