### Some articles on *metric space, space, metric, metric spaces, spaces*:

Discrete Space - Properties

... The underlying uniformity on a discrete

... The underlying uniformity on a discrete

**metric space**is the discrete uniformity, and the underlying topology on a discrete uniform**space**is the ... Thus, the different notions of discrete**space**are compatible with one another ... topology of a non-discrete uniform or**metric space**can be discrete an example is the**metric space**X = {1/n n = 1,2,3...} (with**metric**inherited from the real line and ...Compact Space - Other Forms of Compactness

... which are equivalent to compactness in

... which are equivalent to compactness in

**metric spaces**, but are inequivalent in general topological**spaces**... Every real-valued continuous function on the**space**is bounded ... While all these conditions are equivalent for**metric spaces**, in general we have the following implications Compact**spaces**are countably compact ...Pseudocompact Space - Properties Related To Pseudocompactness

... In order that a Tychonoff

... In order that a Tychonoff

**space**X is pseudocompact it is necessary and sufficient that every locally finite collection of non-empty open sets of X is finite ... Every countably compact**space**is pseudocompact ... For normal Hausdorff**spaces**the converse is true ...Category Of

... In category-theoretic mathematics, Met is a category that has

**Metric Spaces**... In category-theoretic mathematics, Met is a category that has

**metric spaces**as its objects and**metric**maps (continuous functions between**metric**... This is a category because the composition of two**metric**maps is again a**metric**map ... The monomorphisms in Met are the injective**metric**maps, maps that do not map two points into a single point ...Types of

... A

**Metric Spaces**- Compact Spaces... A

**metric space**M is compact if every sequence in M has a subsequence that converges to a point in M ... This is known as sequential compactness and, in**metric spaces**(but not in general topological**spaces**), is equivalent to the topological notions of countable ... Examples of compact**metric spaces**include the closed interval with the absolute value**metric**, all**metric spaces**with finitely many points, and the Cantor set ...### Famous quotes containing the word spaces:

“Every true man is a cause, a country, and an age; requires infinite *spaces* and numbers and time fully to accomplish his design;—and posterity seem to follow his steps as a train of clients.”

—Ralph Waldo Emerson (1803–1882)

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