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Sequential spaces, I | Dan Ma's Topology Blog
https://dantopology.wordpress.com/2010/06/21/sequential-spaces-i
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. Sequential spaces, I. June 21, 2010. Any topological space where there is a countable base at every point is said to satisfy the first axiom of countability or to be first countable. In this post we discuss several properties weaker than the first axiom of countability. All spaces under consideration are Hausdorff. Any first countable space. Satisfies each of the following conditions:. Then there is a sequence.
A Space with G-delta Diagonal that is not Submetrizable | Dan Ma's Topology Blog
https://dantopology.wordpress.com/2012/08/10/a-space-with-g-delta-diagonal-that-is-not-submetrizable
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. A Space with G-delta Diagonal that is not Submetrizable. August 10, 2012. The property of being submetrizable implies having a. Diagonal. There are several other properties lying between these two properties (see [1]). Before diving into these other properties, it may be helpful to investigate a classic example of a space with a. Diagonal that is not submetrizable. The diagonal of a space. A subset of the square.
An exercise gleaned from the proof of a theorem on pseudocompact space | Dan Ma's Topology Blog
https://dantopology.wordpress.com/2015/08/02/an-exercise-gleaned-from-the-proof-of-a-theorem-on-pseudocompact-space
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. An exercise gleaned from the proof of a theorem on pseudocompact space. August 2, 2015. The exercise we wish to highlight deals with continuous one-to-one functions defined on pseudocompact spaces. We first give a brief backgrounder on pseudocompact spaces with links to earlier posts. All spaces considered are Hausdorff spaces. A space. Is a pseudocompact space if every continuous real-valued function defined on.
Several ways to define countably tight spaces | Dan Ma's Topology Blog
https://dantopology.wordpress.com/2015/06/01/several-ways-to-define-countably-tight-spaces
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. Several ways to define countably tight spaces. June 1, 2015. Is countably tight (or has countable tightness) if for each. There is a countable. According to this Wikipedia entry. Be a space. The following statements are equivalent. The set equality (a) holds. If condition (b) holds,. If condition (c) holds,. Statement 1 is the definition of a countably tight space. The set inclusion. Is a sequential space. Is a sequ...
Pseudocompact + Metacompact implies Compact | Dan Ma's Topology Blog
https://dantopology.wordpress.com/2012/08/16/pseudocompact-metacompact-implies-compact
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. Pseudocompact Metacompact implies Compact. August 16, 2012. It is a well known result that any countably compact and metacompact space is compact (see Theorem 5.3.2 in [1]). A discussion of this result is also found in this blog ( countably compact metacompact. Is said to be almost compact if for every open cover. There is a finite. Be a regular space. Then. Is compact if and only if. See Theorem 4B in this post.
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Dan Ma's Topology Blog | Expository Articles In General Topology
Dan Ma's Topology Blog. Expository Articles In General Topology. Skip to primary content. Skip to secondary content. In between G-delta diagonal and submetrizable. March 21, 2018. This post discusses the property of having a. Diagonal and related diagonal properties. The focus is on the diagonal properties in between. Diagonal and submetrizability. The discussion is followed by a diagram displaying the relative strengths of these properties. Some examples and questions are discussed. Is said to be a.
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