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compact
In mathematics, specifically general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (containing all its limit points) and bounded (having all its points lie within some fixed distance of each other).
Examples of compact spaces include a closed real interval, a union of a finite number of closed intervals, a rectangle, or a finite set of points. This notion is defined for more general topological spaces in various ways, which are usually equivalent in Euclidean space but may be inequivalent in other spaces.
One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.
The Bolzano–Weierstrass theorem states that a subset of Euclidean space is compact in this sequential sense if and only if it is closed and bounded.
Thus, if one chooses an infinite number of points in the closed unit interval [0, 1], some of those points will get arbitrarily close to some real number in that space.
For instance, some of the numbers in the sequence 1/2, 4/5, 1/3, 5/6, 1/4, 6/7, … accumulate to 0 (while others accumulate to 1).
The same set of points would not accumulate to any point of the open unit interval (0, 1), so the open unit interval is not compact. Although subsets (subspaces) of Euclidean space can be compact, the entire space itself is not compact since it is not bounded.
For example, considering
R
1
{\displaystyle \mathbb {R} ^{1}}
, the entire real number line, the sequence of points 0, 1, 2, 3, …, has no subsequence that converges to any real number.
Compactness was formally introduced by Maurice Fréchet in 1906 to generalize the Bolzano–Weierstrass theorem from spaces of geometrical points to spaces of functions. Arzelà–Ascoli theorem and the Peano existence theorem exemplify applications of this notion of compactness to classical analysis. Following its initial introduction, various equivalent notions of compactness, including sequential compactness and limit point compactness, were developed in general metric spaces. In general topological spaces, however, these notions of compactness are not necessarily equivalent. The most useful notion—and the standard definition of the unqualified term compactness—is phrased in terms of the existence of finite families of open sets that "cover" the space in the sense that each point of the space lies in some set contained in the family. This more subtle notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, exhibits compact spaces as generalizations of finite sets. In spaces that are compact in this sense, it is often possible to patch together information that holds locally—that is, in a neighborhood of each point—into corresponding statements that hold throughout the space, and many theorems are of this character.
The term compact set is sometimes used as a synonym for compact space, but often refers to a compact subspace of a topological space as well.
Selling off my S&W m2.0 compact magazines. I have 8 total and each are equipped with Floyds custom base pads making them 17 rounds total. All of these are under a year old.
Brand news these would cost $70 each. I am asking $299 obo for all of them.
No trades please.
Excellent condition, maybe 3 mags through it. Comes with: Case, Gun, (1)9-Round Magazine, Manual.
Local pick up preferred. Buyer pays for shipping (if applicable), transfer & background. I accept all payment methods - please add fees if using goods and services.
Preferred...
Selling a CZ P10 Compact chambered in 9mm, it is in excellent condition and comes with the factory case and 2 mags. . Asking $460
This is part of an estate that I am helping the family liquidate, all transfers will be completed at their preferred ffl in Hillsboro, OR. This is a cash only deal...
Selling my two S&W M&P 2.0 9mm (Full size and compact 4")
Both of these have been upgraded, but include all original parts (Base pads, palm swells, sights, and triggers)
The full size comes with the following:
Trijicon night sights
Apex flat trigger
Floyds custom magwell
Floyds Plus 6 base pad...
Selling my concealed carry handgun. Lots of mods on this and selling all of them with the gun.
Well taken care of and very clean.
All original parts included (sights, trigger, basepads)
model: Smith and wesson m&p 2.0 4" 9mm compact 15 round
Add ons:
Floyds Custom magwell (msrp $75)...
S&W M&P 2.0 Compact 4.0" with a manual safety, 15rd flush fit capacity. Has shot flawlessly, maybe 200rds through it.
Includes original box and contents. Can include 1-2 mags for extra in a legal state but I'd rather hold onto them due to being stuck in Washington state.
Also selling...
Looking to pick up any CZ mags that work in a 75 compact. Willing to drive reasonable distances to meet up. I’ve got some 5.56 I’d be willing to trade or just buy outright.
PSA Dagger Compact (G19 clone): 9MM Pistol with Extreme Carry Cut Slide with Night Sights, Flat Dark Earth
-Tear drop extended mag release
-Upgraded night sights
-Extended slide lock
-no magazines
-Less than 50 rounds through it,no issues
Buyer pays any transfer fees (Portland or Vancouver area...
No trades please.
Excellent condition, maybe 3 mags through it. Comes with: Case, Gun, (1)9-Round Magazine, Manual.
Local pick up preferred. Buyer pays for shipping (if applicable), transfer & background. I accept all payment methods - please add fees if using goods and services.
Preferred...
No trades please.
Never fired - like new - excellent condition. Includes everything from the factory: Case/box, mags - (1) 11-rounder & (1) 13-rounder, speed loader, etc.
Local pick up preffered. Buyer pays for shipping (if applicable), transfer & background. I accept all payment methods -...
Both new never shot.
Full size sig module. With mag release Fits 9,40,357
Carry module from Wilson Combat. With mag release. So think a g19 compact grip length. And shorter front nose.
Sig carry mag 9mm with a capacity of 15 rounds.
Trade for...
P320 full sized 4.7 barrel in 357 SIG...
Hello, I'm posting up for sale a PSA dagger compact (G19). Has less than 100rds through it, awesome shooting pistol but I'm reconsolidating my carry caliber.
Will come with 2 magazines, nice hard case and some extra spare parts.
Looking to get $200 or trade towards a Glock plus cash from me...
Looking for subcompact and compact 9mm at reasonable prices. I prefer Glock 43/43X/26 but if you have anything else feel free to PM me.
Portland metro area
I bought it a couple months ago with the intention of it being my wife's EDC; long story short, it is too bulky for her everyday attire so here we are.
Round count is extremely low, maybe 150 if that, shooting all brass. Some light holster wear from dry fire practice but nothing concerning...
Ruger American Compact 308 - 18in with Vortex Crossfire 3-9x40 and a level bubble.
I am throwing in about 55 rds of different types of 308 hunting ammo.
I just want to be upfront that the rifle has some cosmetic damage only on the right side of the barrel due to a leakage of a dehumidifier bag...